3-3 自然科学研究所研究集会報告書

1. 研究集会の名称：The Japanese Conference on Combinatorics and its Applications 2016 (JCCA2016)
2. 主催（共催等）：日本大学文理学部自然科学研究所，ERATO 河原林巨大グラフプロジェクト，国立情報学研究所（京都大学財団）
3. 開催日時：平成 28 年 5 月 21 日（土）から 5 月 25 日（水）までの 5 日間
4. 開催場所：京都大学百周年時計台記念館
5. 担当責任者：森山園子（日本大学文理学部）
河原林健一（国立情報学研究所）
6. 参加者数：166 名
7. 国際会議の趣旨
近年ビッグデータや巨大グラフを扱う技術を支える数学として，組合せ論 combinatorics が注目されている。組合せ論は離散数学，有限数学と同義であり，「有限の対象を扱う数学」である。コンピュータの発達とともに，有限の対象を扱う数学として離散数学 = 組合せ論の必要性が認識され，組合せ論は近年急速に発展してきた。
こうした流れの中で，2014 年に主にグラフ理論を研究する研究者が中心となって，日本大学文理学部自然科学研究所主催，ERATO 河原林プロジェクトの援助の下，日本大学文理学部において国際会議 The Japan Conference onGraph Theory and Combinatorics を開催した。この国際会議にはグラフ理論研究者のみならず，組合せ論の他の分野の研究者も多数参加し，幅広い内容の研究発表と議論がなされた。この成功を受け，2016 年には組合せ論を前面に押し出して，本国際会議を開催した。
招待講演では著名な研究者 9 名に講演を依頼した。彼らの講演を 1 つの国際会議で聴講する機会を提供することで，日本人研究者に資することを狙った。
また今回の国際会議ではミニシンポジウムを開催した。テーマを絞り込んだ研究発表を行うことで，今後の日本の組合せ論発展に重要と思われる分野の活性化を図った。

8. プログラム• 5 月 21 日（土）13:30~14:30 （招待講演）
Hadi Kharaghani (University of Lethbridge, Canada), Bush-type Hadamard matrices andapplications
15:00~15:20 Masahiro Hachimori (University of Tsukuba, Japan), Hereditary properties of simplicial complexes andh-triangles
Jakub Przybyfo (AGH University of Science and Poland), Neighbour distinguishing graph colourings
Technology,Gee-Choon Lau (MARA University of Technology, Malaysia), On SD-prime labeling of graphs
Yi-Hua Yang (National Tsing Hua University, Taiwan), Double-weighted paired-domination on Graphs
15:25~15:45 Aki Mori (Osaka University, Japan), Multibasic Ehrhart theory
Mariusz WoĮniak (AGH University, Poland), On directed versions of 1-2-3 Conjecture
Mania Roswitha (Sebelas Maret University, Indonesia), On Super (a, d)-star-antimagic total labeling ofgeneralized Petersen graph
Christoph Brause (TU Bergakademie Freiberg, Germany), Total domination and the annihilation number ofa graph ̶ on a conjecture of Graffiti.pc
15:50~16:10 Zongchen Chen (Shanghai Jiao Tong University, China), Optimal Arrangements in Euclidean Space58

Tsai-Lien Wong (National Sun Yat-sen University, Taiwan), On total weight choosability of graphs
Titin Sri Martini (Sebelas Maret University, Indonesia), Cycle-Supermagic covering on sunflower graph
Suhadi Wido Saputro (Institut Teknologi Bandung, Indonesia), On locating-dominating number of circulantgraphs
16:15~16:35 Eugen Mandrescu (Holon Institute of Technology, Israel), 1-wellcovered graphs and partial unimodality ofindependence polynomials
Seiya Negami (Yokohama National University, Japan), Bipartite polyhedral maps are disinguishing
3-colorable with few exceptions
Roslan Hasni (Universiti Malaysia Terengganu, Malaysia), On the edge irregularity strength of corona
product of graphs with cycle
Hsin-Hao Lai (National Kaohsiung Normal University, Taiwan), Results on expansion of global secure sets
17:00~18:00 （招待講演）Christos Athanasiadis (University of Athens, Greece), Symmetric, unimodal and gammanonnegative polynomials in combinatorics and geometry• 5 月 22 日（日）9:40~10:40 （招待講演）Richard P. Stanley (Massachusetts Institute of Technology, USA), Smith normal form andcombinatorics
11:00~11:20 Shuya Chiba (Kumamoto University, Japan), On 2-factors through specified perfect matchings in bipartite
graphsKiyoshi Ando (National Institute of Informatics, Japan), Some conditions on G [V 5(G)] for a 5-connected
graph G to have a contractible edge
Bart Sevenster (University of Amsterdam, The Netherlands), Graph parameters from symplectic groupinvariants
Min Yan (Hong Kong University of Science and Technology, Hong Kong), Tiling of the sphere by almost
equilateral pentagons
11:25~11:45 Jan Ekstein (University of West Bohemia, Czech Republic), Connected even factors in the square of 2-edge
connected graphs
Raka Jovanovic (Hamad bin Khalifa University, Qatar), A heuristic approach to dividing graphs into biconnected components of specified size
Rezvan Varmazyar (Islamic Azad University, Iran), On the chromatic number of zero-divisor graphs ofmodules
Huilan Chang (National University of Kaohsiung, Taiwan), Learning a hidden uniform hypergraph
11:50~12:10 Mingquan Zhan (Millersville University of Pennsylvania, USA), On s-hamiltonian line graphs of claw-freegraphs
Henry Liu (Central South University, China), Highly connected subgraphs in sparse graphs
Yoshio Sano (University of Tsukuba, Japan), Travel groupoids and combinatorial structures on a graph
Xuding Zhu (Zhejiang Normal University, China), A variant of hypercube with small diameter59

13:40~14:40 （招待講演）Tomáš Kaiser (University of West Bohemia, Czech Republic), Hamilton cycles in line graphs
ミニシンポジウム：Enumerative Combinatorics
15:00~15:30 Akihiro Higashitani (Kyoto Sangyo University, Japan), Ehrhart polynomials of lattice simplices and linear
binary code
15:45~15:15 Jang Soo Kim (Sungkyunkwan University, Korea), On q-integrals over order polytopes
15:45~15:15 Shuhei Kamioka (Kyoto University, Japan), Triple product formulae for boxed plane partitions derived fromorthogonal polynomials
15:45~15:15 Sen-Peng Eu (National Taiwan Normal University, Taiwan), Evacuation and cyclic sieving on partitions
ミニシンポジウム：Spectral Graph Theory and Related Topics
15:00~15:50 Edwin van Dam (Tilburg University, The Netherlands), Association schemes and almost distance-regulargraphs
16:00~16:20 Sho Kubota (Tohoku University, Japan), Strongly regular graphs with the same parameters as the symplecticgraph
16:20~16:40 Gary Greaves (Tohoku University, Japan), On equiangular lines and regular graphs
16:40~17:00 Akihiro Munemasa (Tohoku University, Japan), On a lower bound on the Laplacian eigenvalues of a graph
17:10~17:30 Jae young Yang (POSTECH, Korea), A generalization of a Hoffman’s theorem
17:30~17:50 Etsuo Segawa (Tohoku University, Japan), Spectral and stochastic behaviors of Grover walks
17:50~18:10 Masato Mimura (Tohoku University, Japan), Multi-way expanders and imprimitive group actions on graphs• 5 月 23 日（月）9:40~10:40 （招待講演）Maria Chudnovsky (Princeton University, USA), Coloring some perfect graphs
11:00~11:20 Yuhei Inoue (Tohoku University, Japan), A new approach to the four color theorem via associahedra
Akihiro Higashitani (Kyoto Sangyo University, Japan), Lattice simplices having small degrees
Joshua E. Ducey (James Madison University, USA), Critical groups of strongly regular graphs
Tomoko Adachi (Toho University, Japan), A cluttered ordering for a bipartite graph
11:25~11:45 Kenta Ozeki (National Institute of Informatics, Japan), Kempe equivalence of 3-edge-coloringsin cubicgraphs on the pro jective plane
Igor Makhlin (National Research University HSE, Russia), FFLV Polytopes and Their Vertices
Mohsen Ghasemi (Urmia University, Iran), 2-arc-transitive graphs of order 4p
Gen Kawatani (Yokohama National University, Japan), On a lower bound graph of a lattice
11:50~12:10 Ju Zhou (Kutztown University of Pennsylvania, USA), Z3-connectivity of triangularly-connected graphs
Akiyoshi Tsuchiya (Osaka University, Japan), Volume of Gorenstein Fano polytopes arising from orderpolytopes and chain polytopes
Shohei Satake (Nagoya University, Japan), Asymmetry of tournaments and some related results
Jobby Jacob (Rochester Institute of Technology, USA), A generalization of vertex rankings of graphs60• 5 月 24 日（火）9:40~10:40 （招待講演）András Sebö (CNRS, Laboratoire G-SCOP, Université Grenoble-Alpes, France), Crossing roads
in combinatorial optimization: The Salesman, The Postman and polyhedra
11:00~11:20 Arnfried Kemnitz (Technical University of Braunschweig, Germany), Sum list colorings of graphs
Dennis Wong (Northwest Missouri State University, USA), A new universal cycle for permutations
Kazuki Matsubara (Chuo Gakuin University, Japan), Some existence of splitting BIB designs
Angelica Klosky (Gettysburg College, USA), Signed sum free sets
11:25~11:45 Chih-Hung Yen (National Chiayi University, Taiwan), On r-equitable coloring of graph products
Mustafa Kemal Tural (Middle East Technical University, Turkey), On the Maximal Matching Polytope
Da Zhao (Shanghai Jiao Tong University, China), On symmetric BIBDs with the same 3-subset multiplicity
Jacob Katriel (Israel Institute of Technology, Israel), Refinement of the structure constants in the class-sum
algebra of the symmetric group
11:50~12:10 Mariusz Meszka (AGH University of Science and Technology, Poland), Maximal edge-colorings of graphs
Chi-Yeh Chen (National Cheng Kung University, Taiwan), Approximation algorithms for the Steiner tree
problem with the bounded edge-length
Li Yun (Soochow University, China), On the existence of S (3, {4, 5, 7}, v)
Narayanan N (Indian Institute of Technology Madras, India), Trees and regularity of binomial edge ideals
13:40~14:40 （招待講演）Chris Godsil (University of Waterloo, Canada), Uniform Mixing and Quantum Walks
ミニシンポジウム：Combinatorics of Hyperplane Arrangements
15:00~15:30 Christos Athanasiadis (University of Athens, Greece), Combinatorics of hyperplane arrangements: Openproblems and recent progress
15:30~16:00 Masahiko Yoshinaga (Hokkaido University, Japan), Linial arrangements and Eulerian polynomials
16:15~16:45 Richard P. Stanley (Massachusetts Institute of Technology, USA), Valid orderings of a real hyperplanearrangement
16:45~17:15 Shuhei Tsujie (Hokkaido University, Japan), A characterization of freeness for ψ-graphical arrangements
17:30~18:00 Takuro Abe (Kyushu University, Japan), Divisional flags and freeness of hyperplane arrangements
ミニシンポジウム：Hadamard Matrices and Combinatorial Designs
15:00~15:50 Richard M. Wilson (California Institute of Technology, USA), Revisiting certain symmetric designs andHadamard difference sets
16:00~16:20 Kohei Yamada (Nagoya University, Japan), Factorizations of cyclic groups and decompositions of a Singer
orbit of a projective line
16:25~16:45 Xiao-Nan Lu (Nagoya University, Japan), On cyclic grid-block designs
16:50~17:10 Sho Suda (Aichi University of Education, Japan), Unbiased orthogonal designs
17:25~17:45 Ha jime Tanaka (Tohoku University, Japan), On tight relative t-designs in hypercubes
17:50~18:10 Bart Litjens (University of Amsterdam, The Netherlands), New upper bounds for nonbinary codes based onquadruples

61ミニシンポジウム：Discrete Convexity and Combinatorial Optimization
15:00~15:30 Takuro Fukunaga (National Institute of Informatics, Japan), Network optimization on unit disk graphs
15:30~16:00 Yutaro Yamaguchi (University of Tokyo, Japan), How to make a bipartite graph DM-irreducible by addingedges
16:10~16:40 Tasuku Soma (The University of Tokyo, Japan), Maximizing monotone submodular functions over theinteger lattice
16:40~17:20 Tamás Király (Eötvös University, Hungary), Arborescence covering problems: structural results andalgorithms
17:30~18:10 Hiroshi Hirai (The University of Tokyo, Japan), Discrete Convex Analysis beyond Zn• 5 月 25 日（水）9:40~10:40 （招待講演）Gary MacGillivray (University of Victoria, Canada), Reconfiguring graph colourings
11:00~11:20 Jirapha Limbupasiriporn (Silpakorn University, Thailand), Codes from neighborhood designs of the graphs
q −1GP (q,) with q odd2
Roman ýada (University of West Bohemia, Czech Republic), On color-degree conditions for long rainbow
paths
Ingo Schiermeyer (Technische Universität Bergakademie Freiberg, Germany), Chromatic number of P5free graphs: χ-binding functions
Giora Dula (Netanya Academic College, Israel), On weighing matrices
11:25~11:45 Jingyuan Chen (Soochow University, China), Combinatorial constructions of optimal (m, n, 4, 2) opticalorthogonal signature pattern Codes
Liming Xiong (Beijing Institute of Technology, China), Forbidden subgraphs and weak locally connectedgraphs
Toshiki Abe (Yokohama National University, Japan), Domination number of outer annulus triangulations
Vincent Va jnovszki (LE2I, Université de Bourgogne FrancheComté, Dijon, France), Bounded growth
functions: Gray codes and exhaustive generation
11:50~12:10 John Vincent S. Morales (Tohoku University, Japan), On Terwilliger algebra of Lee association schemes
over Z4
Hong-Jian Lai (West Virginia University, USA), Supereulerian digraphs
Richard Brewster (Thompson Rivers University, Canada), A Dichotomy theorem for circular colouringreconfiguration
Ivan H. Sudborough (University of Texas at Dallas, USA), On permutation arrays for hamming distance:
improving MOLS bounds
13:40~14:40 （招待講演）Boram Park (Ajou University, Korea), Coloring and list coloring of the squares of graphs
15:00~15:20 Hiroshi Nozaki (UAichi University of Education, Japan), Maxi mal m-distance sets containing therepresentation of the Hamming graph H(n, m)
Jacob Turner (University of Amsterdam, The Netherlands), A faster algorithm for computing Tutte
polynomials of lattice path matroids
Yoshihiro Asayama (Yokohama National University, Japan), On SD-prime labeling of graphs

62

Iwao Sato (Oyama National College of Technology, Japan), A matrix-weighted zeta function of a graph
15:25~15:45 Kyoung-Tark Kim (Shanghai Jiao Tong University, China), Spherical designs of some harmonic indices
Keisuke Shiromoto (Kumamoto University, Japan), On covering numbers of of matroids
Raiji Mukae (National Institute of Technology, Miyakono jo College, Japan), Covering pro jective planargraphs with forests
Hideo Mitsuhashi (Utsunomiya University, Japan), Quaternionic quantum walks and zeta functions ofgraphs
15:50~16:10 Yan Zhu (Shanghai Jiao Tong University, China), Relative t-designs in binary Hamming association schemes
Lili Mu (Dalian University of Technology, China), Catalan-like numbers and Hankel determinants
Carol T. Zamfirescu (Ghent University, Belgium), Hamiltonian properties of polyhedra with few 3-cuts
Sul-young Choi (Le Moyne College, USA), Error correcting code from induced subgraphs of a completegraph Kn63