Hakata Workshop 2014 の履歴(No.8)

Hakata Workshop 2014†

～ Discrete Mathematics and its Applications～

Our purpose of this meeting is giving an opportunity to make a speech and to communicate with researchers who study various fields not only Combinatrics.

Further information is available from the organizers below.

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Organizers†

Yoshihiro Mizoguchi (Kyushu University),
Hayato Waki (Kyushu University),
Takafumi Shibuta (Kyushu University),
Tetsuji Taniguchi (Matsue College of Technology),
Osamu Shimabukuro (Nagasaki University)
Makoto Tagami ( Kyushu Institute of Technology),
Hirotake Kurihara (Kitakyushu National College of Technology)
Shuya Chiba (Kumamoto University)

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Supported by†

Laboratory of Advanced Software in Mathematics, Institute of Mathematics for Industry, Kyushu University
JSPS KAKENHI(Grant-in-Aid for Exploratory Research) Grant Number 25610034.
JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.

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Date†

Saturday, February 8, 2014

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Location†

Seminar Room R (4F) in Reference Eki Higashi Building. 1-16-14 Hakata-Eki-Higashi, Hakata-Ku, Fukuoka City, 812-0013 (see http://www.re-rental.com/ , Google maps )

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Program†

	Speaker	Title
9:25--9:30	Opening (Tetsuji Taniguchi)
9:30--10:20	Shoichi Tsuchiya (Tokyo University of Science)	On Halin graphs and generalized Halin graphs
10:30--11:20	Shuya Chiba (Kumamoto University)	On the number of components of $2$ -factors in claw-free graphs
12:40--14:50	Poster Session (Software in Mathematics Demonstration Track)
15:10--16:00	Michio Seto (Shimane University)	Graph homomorphisms and de Branges-Rovnyak theory
16:10--16:50	TBA	TBA
17:00--17:50	Shun'ichi Yokoyama (Kyushu University)	Computing resultant matrix of general multivariate polynomials and its determinant using Magma
17:50--18:00	Closing (Yoshihiro Mizoguchi)

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List of Poster session speakers †

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Abstract†

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Shoichi Tsuchiya†

Title: On Halin graphs and generalized Halin graphs
Abstract: A Halin graph, defined by Halin, is a plane graph $H=T \cup C$ such that $T$ is a spanning tree of $H$ with no vertices of degree $2$ where $|T|\geq 4$ and $C$ is a cycle whose vertex set is the set of leaves of $T$ . On the other hand, generalized Halin graph is a graph $H=T \cup C$ such that $T$ is a spanning tree of $H$ with no vertices of degree $2$ where $|T|\geq 4$ and $C$ is a cycle whose vertex set is the set of leaves of $T$ . Note that some generalized Halin graphs may not be plane graphs, (for example, Petersen graph is a generalized Halin graph which is not planar). In this talk, we introduce some known results on Halin graphs and generalized Halin graphs. After that, we investigate difference between Halin graphs and generalized Halin graphs.

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Shuya Chiba†

Title: On the number of components of $2$ -factors in claw-free graphs
Abstract: We consider only finite graphs without loops. A graph $G$ is said to be claw-free if $G$ has no induced subgraph isomorphic to $K_{1$ (here $K_{1$ denotes the complete bipartite graph with partite sets of cardinalities $1$ and $3$ , respectively). A $2$ -factor of a graph $G$ is a spanning subgraph of $G$ in which every component is a cycle. It is a well-known conjecture that every $4$ -connected claw-free graph is Hamiltonian due to Matthews and Sumner [Hamiltonian results in $K_{1$ -free graphs, J. Graph Theory 8 (1984) 139--146]. Since a Hamilton cycle is a $2$ -factor with one component, there are many results on the upper bounds of the number of components in $2$ -factors of claw-free graphs. In this talk, we will present some recent results on the relationship between the number of components of a $2$ -factor and the minimum degree of a graph.

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Michio Seto†

Title: Graph homomorphisms and de Branges-Rovnyak theory
Abstract: In 1960's, de Branges and Rovnyak developed a theory dealing with Hilbert space embedding $H_1$ $\rightarrow$ $H_2$ . In this talk, comparing with theory of univalent functions, a de Branges-Rovnyak framework for study of graph homomorphisms will be suggested. This is joint work with S. Suda and T. Taniguchi.

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Shun'ichi Yokoyama†

Title: Computing resultant matrix of general multivariate polynomials and its determinant using Magma
Abstract: We produce an efficient program package to compute the resultant matrix and its determinant for a given pair of multivariate polynomials on Magma. This package works much more faster than the Magma's built-in function "Resultant" for multivariate polynomials. We also explain some applications of this package, and especially, try some benchmark problem for computing general formula of the discriminant. This work is in cooperation with Kinji Kimura (Kyoto University).