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20130126 の履歴(No.15)

Hakata Workshop 2013†

～ Combinatrics and its Applications～

THIS IS A PROVISIONAL VERSION

 

This is a satellite seminar of the 11th Japan-Korea Workshop on Algebra and Combinatorics . Our purpose of this meeting is giving an opportunity to make a speech and to commuticate with reserchers who study verious fields not only Combinatorics.

Further information is available from the organizers below.

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Organizers†

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Supported by†

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Date†

  • January 26, 2013. 9:30-18:00
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Location†

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Program†

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January 26 (Saturday) at Room I in Reference Eki Higashi Building.†

  • 9:30--10:05 Akihiro Munemasa (Tohoku University)
    • Complex Hadamard matrices contained in a Bose-Mesner algebra
  • 11:00--11:35 Michael Dobbins (GAIA, Postech)
    • Reducing combinatorial to projective equivalence in realizability problems for polytopes.
  • 11:40--12:15 Aleksandar Jurišić (University of Ljubljana)
    • TBA
  • 12:20--15:10 Poster Session 「数学ソフトウェア紹介」(Introduction to Mathematical Software) (and break)
    • TBA
  • 15:15--16:15 Xiao-Dong Zhang (Shanghai Jiao Tong University)
    • The algebraic connectivity of graphs
  • (break)
  • 16:30--17:05 Katsuhiro Ota (Keio University)
    • Clique minors, chromatic numbers for degree sequences
  • 17:10--17:45 Yota Otachi (JAIST)
    • The path-distance-width of hypercubes
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Abstract†

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Akihiro Munemasa (Tohoku University)†

  • Title:Complex Hadamard matrices contained in a Bose-Mesner algebra
  • Abstract:

A complex Hadamard matrix is an n by n matrix with complex entries with absolute value 1, such that rows are pairwise orthogonal with respect to the hermitian inner product. Recently, Ada Chan constructed a 15 by 15 complex Hadamard matrix using the adjacency matrix of the line graph of the Petersen graph. We found another such matrix, and then generalized it to an infinite family. In this talk, we focus on how to set up a system of polynomial equations for solving this kind of problem more efficiently than the naive approach. This is achieved by determining the ideal of the 3-dimensional algebraic variety consisting of the points of the form in the 6-dimensional space. This is a joint work with Takuya Ikuta.

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Michael Dobbins (GAIA, Postech)†

  • Title:Reducing combinatorial to projective equivalence in realizability problems for polytopes.
  • Abstract:

Determining if there is a polytope of any combinatorial type that satisfies some given property is made difficult by the fact that there are polytopes with realization spaces that are homotopic to any primary semialgebraic set. I will show how, for certain properties, this can be reduced to finding such realizations among projective equivalence classes of polytopes, which are much nicer spaces. An application of this answers a question posed by Bernt Lindström in 1971, that there does exist a polytope without an antiprism.

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Xiao-Dong Zhang (Shanghai Jiao Tong University)†

  • Title:The algebraic connectivity of graphs
  • Abstract:

Let be a simple graph of order and be its Laplacian matrix, where and are the degree diagonal and adjacency matrices, respectively. The the second smallest eigenvalue of is called the algebraic connectivity of In this talk, we survey some new results and progress on the algebraic connectivity. In particular, we present some relationships between the algebraic connectivity and the graph parameters, such as the clique number, the matching number, the independence number, the isoperimetric number, etc.

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Katsuhiro Ota (Keio University)†

  • Title:Clique minors, chromatic numbers for degree sequences
  • Abstract:

For a given graph , let and denote the chromatic number, and the maximum size of clique minors of , respectively. The well-known Hadwiger's conjecture (1943) states that holds for every graph , which is wide open for the graphs with . In 2005, Robertson posed the "Hadwiger's conjecture for degree sequences." For a graphical degree sequence , let and denote the maximum and , respectively, among the graphs having degree sequence . Robertson's conjecture states that for any degree sequence . This conjecture was recently confirmed by Dvořák and Mohar by showing strongly that , where is the maximum size of topological clique minors of graphs having degree sequence . In this talk, we give an alternative and very short proof of Robertson's conjecture. Also, we shall discuss the values of , and for some . These results are based on a joint work with Guantao Chen and Ryo Hazama.

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Yota Otachi (JAIST)†

  • Title: The path-distance-width of hypercubes
  • Abstract:

The path-distance-width of a connected graph is the minimum integer satisfying that there is a nonempty subset of such that the number of the vertices with distance from is at most for any nonnegative integer . We present a general lower bound on the path-distance-width of graph, and determine the path-distance-width of hypercubes by using the lower bound. We also discuss the applicability of the lower bound to other graphs.