2018 International Conference on Graph Theory, Combinatorics and...
Transcript of 2018 International Conference on Graph Theory, Combinatorics and...
2018 International Conference on Graph Theory,
Combinatorics and Applications
Zhejiang Normal University, 688 Yingbin Road, Jinhua, Zhejiang Province, China
October 27-28, 2018
Oct. 27 (地点:数理与信息工程学院第一报告厅)
Chairman: Douglas West
8:30-9:30 Speaker:
Jaroslav Nešetřil
Zhejiang Normal University, China
Charles University, Czech
Title: Graphs and orderings
9:30-10:30 Speaker:
Genghua Fan
Fuzhou University, China
Title: Flows and circuit covers in signed graphs
10:30-11:00 Photo and Tea Break
Chairman: Zhiquan Hu
11:00-11:30
Speaker: Yuejian Peng
Hunan University, China
Title: 3-colored asymmetric bipartite Ramsey number of
connected matchings and cycles
11:30-12:00 Speaker:
Rong Chen
Fuzhou University, China
Title: Three classes of matroids associated with graphs
12:00-13:30 Lunch
Chairman: Jie Ma
13:30-14:30 Speaker:
Baogang Xu
Nanjing Normal University, China
Title: Some results on chromatic number and forbidden holes
Chairman: Rongxia Hao
14:30-15:00 Speaker:
Uwe Schauz
Xi’an Jiaotong-Liverpool University, China
Title: Computing the list chromatic index of graphs
15:00-15:30
Speaker: Xinmin Hou
University of Science and Technology of China, China
Title: On perfect matching coverings and even subgraph
coverings
15:30-16:00 Tea Break
Chairman: Qizhong Lin
16:00-16:30 Speaker:
Xin Zhang
Xidian University, China
Title: Equitable vertex arboricity of graphs
16:30-17:00 Speaker:
Xing Peng
Tianjin University, China
Title: An extension of Erdős-Gallai theorem with applications
Oct. 28 (地点:数理与信息工程学院第一报告厅)
Chairman: Weifan Wang
8:30-9:30 Speaker:
Gennian Ge
Capital Normal University, China
Title: Sparse hypergraphs: from theory to application
9:30-10:30
Speaker: Jan Kratochvil
Charles University, Czech
Title: Geometric intersection graphs: from interval graphs to
string graphs
10:30-11:00 Tea Break
Chairman: Min Chen
11:00-11:30 Speaker:
Seog-Jin Kim
Konkuk University, Korea
Title: Signed colouring and list colouring of k-chromatic graphs
11:30-12:00 Speaker:
Tao Wang
Henan University, China
Title: Cover and variable degeneracy
12:00-13:30 Lunch
Chairman: Daqing Yang
13:30-14:30 Speaker:
Jarosław Grytczuk
Warsaw University of Technology, Poland
Title: From 1-2-3 conjecture to Riemann Hypothesis
Chairman: Huajun Zhang
14:30-15:00
Speaker: Young Soo Kwon
Yeungnam University, Korea
Title: t-common list colorings and some variations of list
colorings
15:00-15:30
Speaker: Yian Xu
The University of Western Australia, Australia
Title: Normal and non-normal Cayley graphs for isomorphic
regular groups
15:30-16:00 Tea Break
Chairman: Huifang Yan
16:00-16:30 Speaker:
Yezhou Wu
Zhejiang University, China
Title: Shortest circuit covers of signed graphs
16:30-17:00 Speaker:
Suijie Wang
Hunan University, China
Title: Linear bounds on characteristic polynomials of matroids
Contents
Plenary Talks
Genghua Fan, Flows and circuit covers in signed graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Gennian Ge, Sparse hypergraphs: from theory to application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Jaros law Grytczuk, From 1-2-3 conjecture to Riemann Hypothesis . . . . . . . . . . . . . . . . . . . . . . 2
Jan Kratochvil, Geometric intersection graphs: from interval graphs to string graphs . . 2
Jaroslav Nesetril, Graphs and orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Baogang Xu, Some results on chromatic number and forbidden holes . . . . . . . . . . . . . . . . . . . . 3
Invited Talks
Rong Chen, Three classes of matroids associated with graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Xinmin Hou, On perfect matching coverings and even subgraph coverings . . . . . . . . . . . . . . . 4
Seog-Jin Kim, Signed colouring and list colouring of k-chromatic graphs . . . . . . . . . . . . . . . . . 5
Young Soo Kwon, t-common list colorings and some variations of list colorings . . . . . . . . . 5
Xing Peng, An extension of Erdos-Gallai theorem with applications . . . . . . . . . . . . . . . . . . . . . 6
Yuejian Peng, 3-colored asymmetric bipartite Ramsey number of connected matchings
and cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Uwe Schauz, Computing the list chromatic index of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Suijie Wang, Linear bounds on characteristic polynomials of matroids . . . . . . . . . . . . . . . . . . . 7
Tao Wang, Cover and variable degeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Yezhou Wu, Shortest circuit covers of signed graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Yian Xu, Normal and non-normal Cayley graphs for isomorphic regular groups . . . . . . . . . 9
Xin Zhang, Equitable vertex arboricity of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Plenary Talks
Flows and circuit covers in signed graphs
Genghua Fan
Fuzhou University, China
Abstract
A signed graph G is a graph associated with a mapping σ: E(G) → {+1,−1}. Signedgraphs can be used to present surface duals of digraphs embedded in non-orientable sur-faces. A signed graph is coverable if each edge is contained in some signed circuit. Theedges of a signed circuit in a signed graph corresponds a minimal dependent set in thesigned graphic matroid. An oriented signed graph (bidirected graph) has a nowhere-zerointeger flow if and only if it is coverable. A signed circuit cover of G is a collection ofsigned circuits which covers all the edges of G. Signed circuit covers is a new topic drawingattention in recent years. In this talk, we give a brief survey of known results and openproblems on signed circuit covers of signed graphs.
Sparse hypergraphs: from theory to application
Gennian Ge
Capital Normal University, China
Abstract
More than forty years ago, Brown, Erdos and Sos introduced the function fr(n, v, e)to denote the maximum number of edges in an r-uniform hypergraph on n vertices whichdoes not contain e edges spanned by v vertices. They posed a well-known conjecture:nk−o(1) < fr(n, e(r − k) + k + 1, e) = o(nk) holds for all integers r > k ≥ 2, e ≥ 3. Notethat for r = 3, e = 3, k = 2, this conjecture was solved by the famous Ruzsa-Szemeredi’s(6,3)-theorem. We add more evidence for the validity of this conjecture. On one hand,we use the hypergraph removal lemma to prove that the upper bound is true for all fixedintegers r ≥ k+ 1 ≥ e ≥ 3. On the other hand, we use tools from additive number theoryto show that the lower bound is true for r ≥ 3, k = 2 and e = 4, 5, 7, 8.
We also use the theory of sparse hypergraphs to attack several open problems andconjectures in cryptography. In particular, we use the (6,3)-theorem to solve a conjectureof Walker and Colbourn on perfect hash families. This conjecture had been open for tenyears and traditional methods seem to have limited effect on it.
1
From 1-2-3 conjecture to Riemann Hypothesis
Jaros law Grytczuk
Warsaw University of Technology, Poland
Abstract
The following, innocently looking question was asked in [1]: Can the edges of anynon-trivial graph be assigned weights from {1, 2, 3} so that adjacent vertices have differentsums of incident edge weights? There exist many variations on this problem in whichone tries to get a graph coloring by other manipulations on vertex degrees. It turns out,unexpectedly, that one of them is related to some deep number theoretic problems, likeGraham’s gcd-problem, Erdos Discrepancy Problem, or even the Riemann Hypothesis.
References
[1] M. Karonski, T. Luczak, and A. Thomason, Edge weights and vertex colours, J Combin
Theory Ser B 91 (2004), 151–157.
Geometric intersection graphs: from interval graphs to string graphs
Jan Kratochvil
Charles University, Czech Republic
Abstract
Intersection representations of graphs are a natural way of graph and network visu-alization. At the same time the classes of graphs that arise in this way are popular andwell studied for their interesting and elegant structural, as well as algorithmic properties.The oldest and best understood of them are interval graphs, i.e., intersection graphs ofintervals on a real line, while the most general are string graphs, i.e., intersection graphsof curves in the plane. A rich universe of intersection defined classes of graphs, describedby geometric properties of the representations lies between these extremal classes.
In the talk, I will survey known results on these classes of graphs, show some of theirelegant properties and proofs and discuss new as well as persisting open problems. Theclasses considered will include but not be restricted to interval, circle, circular arc, func-tion, trapezoid, segment intersection and convex set intersection graphs. The questionsposed will concern recognition, complexity of optimization problems restricted to theseclasses, simultaneous representability and representability of planar graphs.
2
Graphs and orderings
Jaroslav Nesetril
Zhejiang Normal University, China
Charles University, Czech Republic
Abstract
Ordered graph is a graph with linearly ordered vertices. Isomorphisms, subgraphsand homomorphisms should then preserve not only edges but also orderings, i.e. thecorresponding mappings should be monotone.
Which ordered graphs are unavoidable in any ordering of an (unordered) graph? Wesurvey the development of this area which was recently revitalized in yet another context.
Some results on chromatic number and forbidden holes
Baogang Xu
Nanjing Normal University, China
Abstract
A hole is an induced cycle of length at least 4. In this talk, we will present some resultsand open problems on chromatic number and forbidden holes.
3
Invited Talks
Three classes of matroids associated with graphs
Rong Chen
Fuzhou University, China
Abstract
Frame matroids and lifted-graphic matroids are matroids defined using graphs. Theyare two very important classes of matroids, in part due to their prominent role in theMatroid Minor Project. Recently Geelen, Gerards, and Whittle completed the first formalstudy of the class of so-called quasi-graphic matroids, which describes a spectrum ofmatroids contained between frame matroids and lifted-graphic matroids. The three classesof matroids are minor-closed, each of which generalises the class of graphic matroids andexhibits clear graph structure. In this talk, I will introduce some recent results, problems,and conjectures related to the three classes of matroids. No background on matroid theoryis required for the audience.
On perfect matching coverings and even subgraph coverings
Xinmin Hou
University of Science and Technology of China, China
Abstract
A perfect matching covering of a graph G is a set of perfect matchings of G such thatevery edge of G is contained in at least one member of it. Berge conjectured that everybridgeless cubic graph admits a perfect matching covering of order at most five (we callsuch a collection of perfect matchings a Berge covering of G). A cubic graph G is called aKotzig graph if G has a 3-edge-coloring such that each pair of colors form a hamiltoniancircuit (introduced by Haggkvist and Markstrom, JCTB 2006). In this talk, we prove thatif there is a vertex w of a cubic graph G such that G− w, the graph obtained from G−wby suppressing all degree two vertices, is a Kotzig graph, then G has a Berge covering. Wealso obtain some results concerning the so-called 5-even subgraph double cover conjecture.(Joint work with Hong-Jian Lai and Cun-Quan Zhang)
4
Signed colouring and list colouring of k-chromatic graphs
Seog-Jin Kim
Konkuk University, Korea
Abstract
A signed graph is a pair (G, σ), where G is a graph and σ : E(G) → {1,−1} is asignature of G. A set S of integers is symmetric if i ∈ S implies that −i ∈ S. Ak-colouring of (G, σ) is a mapping f : V (G) → Nk such that for each edge e = uv,f(x) 6= σ(e)f(y), where Nk is a symmetric integer set of size k. We define the signedchromatic number of a graph G to be the minimum integer k such that for any signatureσ of G, (G, σ) has a k-colouring. Let f(n, k) be the maximum signed chromatic number ofan n-vertex k-chromatic graph. This paper determines the value of f(n, k) for all positiveintegers n ≥ k. Then we study list colouring of signed graphs. A list assignment L of Gis called symmetric if L(v) is a symmetric integer set for each vertex v. The weak signedchoice number chw±(G) of a graph G is defined to be the minimum integer k such that forany symmetric k-list assignment L of G, for any signature σ on G, there is a proper L-colouring of (G, σ). We prove that the difference chw±(G)−χ±(G) can be arbitrarily large.On the other hand, chw±(G) is bounded from above by twice the list vertex arboricity ofG. Using this result, we prove that chw±(K2?n) = χ±(K2?n) = d2n
3 e + b2n3 c. This is joint
work with Ringi Kim and Xuding Zhu.
t-common list colorings and some variations of list colorings
Young Soo Kwon
Yeungnam University, Korea
Abstract
In this talk, we introduce t-common list colorings and some variation of list colorings.For a graph G and for a given nonnegative integer t, a t-common list assignment of G isa mapping L from V (G) to all subsets of S for a set of colors S, such that given t colorsbelong to L(v) for every v ∈ V (G). The t-common list chromatic number of G denoted bycht(G) is defined as the minimum positive integer k such that there exists an L-coloringof G for every t-common list assignment L of G, satisfying |L(v)| ≥ k for every vertexv ∈ V (G). We show that for all positive integers k, ` with 2 ≤ k ≤ ` and i1, i2, . . . , ik−2
with k ≤ ik−2 ≤ · · · ≤ i1 ≤ `, there exists a graph G such that χ(G) = k, ch(G) = ` andcht(G) = it for every t = 1, . . . , k− 2. Moreover, we consider the t-common list chromaticnumber of planar graphs. By constructing a planar graph G such that ch1(G) = 5, weshow that the sharp upper bound for 1-common list chromatic number of planar graphsis 5. We also give some properties related to some variations of list colorings and suggestseveral questions related to these colorings.
5
An extension of Erdos-Gallai theorem with applications
Xing Peng
Tianjin University,China
Abstract
The famous Erdos-Gallai theorem gives an upper bound on the maximum number ofedges in graphs with given circumference. In this talk, we will first present an extensionof Erdos-Gallai theorem. Then we will discuss several applications of this extension tothe generalized Turan number and the consecutive length of cycles in graphs. Joint workwith Bo Ning.
3-colored asymmetric bipartite Ramsey number of connected matchings
and cycles
Yuejian Peng
Hunan University, China
Abstract
Let k, l,m be integers and r(k, l,m) be the minimum integer N such that for any red-blue-green coloring of KN,N , there is a red matching of size at least k in a component, ora blue matching of at least size l in a component, or a green matching of size at least min a component. We determine the exact value of r(k, l,m) completely which answers aquestion of Bucic, Letzter, and Sudakov. Applying a technique originated by Luczak thatapplies Szemeredi’s Regularity Lemma to reduce the problem of showing the existence of amonochromatic cycle to show the existence of a monochromatic matching in a component,we obtain the 3-colored asymmetric bipartite Ramsey number of cycles asymptotically.This is a joint work with Zhidan Luo.
6
Computing the list chromatic index of graphs
Uwe Schauz
Xi’an Jiaotong-Liverpool University, China
Abstract
As starting point, we formulate a corollary to the Quantitative Combinatorial Nullstel-lensatz. This corollary does not require the consideration of any coefficients of polynomi-als, only evaluations of polynomial functions. In certain situations, our corollary is moredirectly applicable and more ready-to-go than the Combinatorial Nullstellensatz itself. Itis also of interest from a numerical point of view. We use it to explain a well-known con-nection between the sign of 1-factorizations (edge colorings) and the List Edge ColoringConjecture. For efficient calculations and a better understanding of the sign, we thenintroduce and characterize the sign of single 1-factors. We show that the product overall signs of all the 1-factors in a 1-factorization is the sign of that 1-factorization. Usingthis result in an algorithm, we attempt to prove the List Edge Coloring Conjecture for allgraphs with up to 10 vertices. This leaves us with some exceptional cases that need to beattacked with other methods.
Linear bounds on characteristic polynomials of matroids
Suijie Wang
Hunan University, China
Abstract
Let χ(t) = a0tn−a1t
n−1+· · ·+(−1)rartn−r be the chromatic polynomial of a graph, the
characteristic polynomial of a matroid, or the characteristic polynomial of an arrangementof hyperplanes. For any integer k = 0, 1, . . . , r and real number x ≥ k − r − 1, we obtaina linear bound of the coefficient sequence, that is(
r + x
k
)≤
k∑i=0
ai
(x
k − i
)≤(m+ x
k
),
where m is the size of the graph, matroid, or hyperplane arrangement. It extends Whit-ney’s sign-alternating theorem, Meredith’s upper bound theorem, and Dowling and Wil-son’s lower bound theorem on the coefficient sequence. In the end, we also propose aproblem on the combinatorial interpretation of the above inequality.
7
Cover and variable degeneracy
Tao Wang
Henan University, China
Abstract
Let f be a nonnegative integer valued function on the vertex-set of a graph. A graphis strictly f-degenerate if each subgraph Γ has a vertex v such that degΓ(v) < f(v). Inthis paper, we define a new concept, strictly f -degenerate transversal, which generalize listcoloring, (f1, f2, . . . , fκ)-partition, signed coloring, DP-coloring and L-forested-coloring.A cover of a graph G is a graph H with vertex set V (H) =
⋃v∈V (G)Xv, where Xv =
{ (v, 1), (v, 2), . . . , (v, κ) }; the edge set M =⋃uv∈E(G) Muv, where Muv is the set of edges
between Xu and Xv, and it is a matching. A vertex set R ⊆ V (H) is a transversal of H if|R∩Xv| = 1 for each v ∈ V (G). A transversal R is a strictly f-degenerate transversalif H[R] is strictly f -degenerate. The main result is a degree type result, which generalizeBrooks’ theorem, Gallai’s theorem, degree-choosable, signed degree-colorable, DP-degree-colorable. Similar to Borodin, Kostochka and Toft’s variable degeneracy, the degree typeresult is also self-strengthening. Using these results, we can uniformly prove many newand known results.
Shortest circuit covers of signed graphs
Yezhou Wu
Zhejiang University, China
Abstract
A signed graph is a graph G associated with a mapping σ : E(G)→ {1,−1}, denotedby (G, σ). A cycle of (G, σ) is a connected 2-regular subgraph. A cycle C is positive if ithas an even number of negative edges, and negative otherwise. The definition of circuitof signed graph comes from the signed-graphic matroid. A circuit cover of (G, σ) is afamily of positive cycles and barbells covering all edges of (G, σ). A circuit cover withthe smallest total length is called a shortest circuit cover. Bouchet proved that a signedgraph with a circuit cover if and only if it has a nowhere-zero integer flow. In this talk,we introduce some recent developments of the shortest circuit covers of signed graphs.
This is joint work with Dong Ye.
8
Normal and non-normal Cayley graphs for isomorphic regular groups
Yian Xu
The University of Western Australia, Australia
Abstract
A Cayley graph Γ = Cay(G,S) is an NNN-graph for G if it is both normal and non-normal for regular subgroups isomorphic to G, that is, Aut(Γ) contains two isomorphicregular subgroups G,H where G is normal in Aut(Γ) and H is non-normal in Aut(Γ). Agroup G has the NNN-property if there exists an NNN-graph for G. It is known that theNNN-graphs are very rare, and only few examples are known. In this talk, we show thatmore NNN-graphs can be obtained by taking graph products on known NNN-graphs, inparticular, we show that the simple groups do not have the NNN-property and Zn doesnot have the NNN-property if 2 | n and 4 - n.
Equitable vertex arboricity of graphs
Xin Zhang
Xidian University, China
Abstract
The vertex arboricity a(G) of a graph G is the minimum number of subsets into whichthe vertex set V (G) can be partitioned so that each subset induces a forest. This notionwas introduced by Chartrand and Kronk [J. London Math. Soc., 44 (1969) 612-616], whoproved that a(G) ≤ 3 for every planar graph. Naturally we can consider the equitableversion of vertex arboricity when we restrict the partition to be an equitable one, thatis, a partition so that the size of each subset is either d|G|/ke or b|G|/kc. If the set ofvertices of a graph G can be equitably partitioned into k subsets such that each subset ofvertices induce a forest of G, then we call that G admits an equitable tree-k-coloring. Theminimum integer k such that G has an equitable tree-k-coloring is the equitable vertexarboricity aeq(G) of G. The notion of equitable vertex arboricity was first introduced byWu, Zhang and Li [Discrete Mathematics, 313 (2013) 2696–2701]. In this talk, I introducethe recent progress on this direction and present some of our new results.
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List of ParticipantsName Institution Email
1 Shenxiao Bao Zhejiang Normal University [email protected] Yuehua Bu Zhejiang Normal University [email protected] Jiaojiao Cao Zhejiang Normal University [email protected] Dong Chen Zhejiang Normal University [email protected] Min Chen Zhejiang Normal University [email protected] Rong Chen Fuzhou University [email protected] Wenwen Chen Zhejiang Normal University [email protected] Xiuyang Chen Zhejiang Normal University [email protected] Yaxue Chen Zhejiang Normal University [email protected] Shuyu Cui Zhejiang Normal University [email protected] Genghua Fan Fuzhou University [email protected] Xuqian Fang Zhejiang Normal University [email protected] Yuping Gao Lanzhou University [email protected] Gennian Ge Capital Normal University [email protected] Jarosław Grytczuk Warsaw University of Technology, Poland [email protected] Xueyao Gui Zhejiang Normal University [email protected] Jianxiu Hao Zhejiang Normal University [email protected] Rongxia Hao Beijing Jiaotong University [email protected] Jingxiang He Zhejiang Normal University [email protected] Jianfeng Hou Fuzhou University [email protected]
21 Xinmin Hou University of Science and Technology of China [email protected]
22 Xiaolan Hu Central China Normal University [email protected] Zhiquan Hu Central China Normal University [email protected] Danjun Huang Zhejiang Normal University [email protected] Nan Jiang Zhejiang Normal University [email protected] Yiting Jiang Zhejiang Normal University [email protected] Ligang Jin Zhejiang Normal University [email protected] Zemin Jin Zhejiang Normal University [email protected] Seog-Jin Kim Konkuk University, Korea [email protected] Jan Kratochvil Charles University, Czech Republic [email protected] Young Soo Kwon Yeungnam University, Korea [email protected] Chunmiao Li Zhejiang Normal University [email protected] Fengwei Li Shaoxing University [email protected] Xueliang Li Nankai University [email protected] Xuer Li Zhejiang Normal University [email protected] Yang Li Soochow University [email protected]
Name Institution Email37 Yuan Li Zhejiang Normal University [email protected] Kai Lin Zhejiang Normal University [email protected] Qizhong Lin Fuzhou University [email protected] Hanquan Liu Zhejiang Normal University [email protected] Juan Liu Zhejiang Normal University [email protected] Min Liu Zhejiang Normal University [email protected] Pengcheng Liu Zhejiang Normal University [email protected] Huajing Lu Zhejiang Normal University [email protected] Quanfeng Lu Zhejiang Normal University [email protected] You Lu Northwestern Polytechnical University [email protected] Kaiyi Luo Zhejiang Normal University [email protected] Xinzhong Lv Zhejiang Normal University [email protected]
49 Jie Ma University of Science and Technology of China [email protected]
50 Huiqun Mao Zhejiang Normal University [email protected]
51 Jaroslav Nešetřil Zhejiang Normal University, ChinaCharles University, Czech Republic [email protected]
52 Xing Peng Tianjin University [email protected] Yuejian Peng Hunan University [email protected] Jingran Qi Zhejiang Normal University [email protected] Pu Qiao East China Normal University [email protected] Uwe Schauz Xi'an Jiaotong-Liverpool University [email protected] Tingting Shan Zhejiang Normal University [email protected]
58 Ce Shi Shanghai Lixin University of Accounting and Finance [email protected]
59 Guixian Tian Zhejiang Normal University [email protected] Chao Wang Zhejiang Normal University [email protected] Chengmin Wang Taizhou University [email protected] Fang Wang Zhejiang Normal University [email protected] Jiaqi Wang Zhejiang Normal University [email protected] Kan Wang Zhejiang Normal University [email protected] Suijie Wang Hunan University [email protected] Tao Wang Henan University [email protected] Weifan Wang Zhejiang Normal University [email protected] Xiaofang Wang Zhejiang Normal University [email protected] Yang Wang Zhejiang Normal University [email protected] Ying Wang Zhejiang Normal University [email protected] Yingqian Wang Zhejiang Normal University [email protected]
Name Institution Email72 Douglas B. West Zhejiang Normal University [email protected] Jianglin Wu Zhejiang Normal University [email protected] Yezhou Wu Zhejiang University [email protected] Wenjing Xia Zhejiang Normal University [email protected] Liqiong Xu JiMei University [email protected] Wen Xu Zhejiang Normal University [email protected] Baogang Xu Nanjing Normal University [email protected] Miaodi Xu Zhejiang Normal University [email protected] Ting Xu Zhejiang Normal University [email protected] Yian Xu The University of Western Australia [email protected] Huifang Yan Zhejiang Normal University [email protected] Jiayan Yan Zhejiang Normal University [email protected] Daqing Yang Zhejiang Normal University [email protected] Wanshun Yang Zhejiang Normal University [email protected] Yirong Yang Zhejiang Normal University [email protected] Pingkang Yu Zhejiang Normal University [email protected] Yao Yu Zhejiang Normal University [email protected] Xingzhi Zhan East China Normal University [email protected] Heng Zhang Zhejiang Normal University [email protected] Huajun Zhang Zhejiang Normal University [email protected] Huijuan Zhang Zhejiang Normal University [email protected] Jinrong Zhang Zhejiang Normal University [email protected] Lu Zhang Zhejiang Normal University [email protected] Mengting Zhang Zhejiang Normal University [email protected] Qian Zhang Zhejiang Normal University [email protected] Xiaoxiu Zhang Zhejiang Normal University [email protected] Xin Zhang Xidian University [email protected] Xuemei Zhang Zhejiang Normal University [email protected] Lina Zheng Zhejiang Normal University [email protected] Lu Zheng Zhejiang Normal University [email protected] Kangyun Zhong Zhejiang Normal University [email protected] Hao Zhou Zhejiang Normal University [email protected] Aina Zhu Zhejiang Normal University [email protected] Chaojie Zhu Zhejiang Normal University [email protected] Jialu Zhu Zhejiang Normal University [email protected] Junlei Zhu Zhejiang Normal University [email protected] Lijuan Zhu Zhejiang Normal University [email protected] Xuding Zhu Zhejiang Normal University [email protected]