# Hakata Workshop 2014

Last-modified: 2014-02-04 (火) 17:34:08 (1692d)

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## 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 Combinatorics.

Further information is available from the organizers below.

### 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)

### 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.

### Date †

Saturday, February 8, 2014

### 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 )

### Program †

Speaker | Title | |
---|---|---|

9:15--9:20 | Opening (Tetsuji Taniguchi) | |

9:20--10:00 | Shoichi Tsuchiya (Tokyo University of Science) | On Halin graphs and generalized Halin graphs |

10:10--10:50 | Shuya Chiba (Kumamoto University) | On the number of components of -factors in claw-free graphs |

11:00--11:40 | Masashi Shinohara (Shiga University) | On complementary Ramsey numbers |

13:10--14:40 | Poster Session (Software in Mathematics Demonstration Track) | |

15:00--15:40 | Michio Seto (Shimane University) | Graph homomorphisms and de Branges-Rovnyak theory |

15:50--16:30 | Jong Hyeon Seo (Pusan National University) | The Convergence of Relaxed Functional Iterations for Solving Quadratic Matrix Equations with an -matrix |

16:40--17:20 | Shun'ichi Yokoyama (Kyushu University) | Computing resultant matrix of general multivariate polynomials and its determinant using Magma |

17:20--17:30 | Closing (Yoshihiro Mizoguchi) |

### List of Poster session speakers †

#### Software in Mathematics Demonstration Track †

- 岩下 寛弥 (九州大学大学院工学府海洋システム工学専攻) HEAPモデル法によるプル型スケジューリングプログラム
- 山岡 幸高 (九州大学数理学府) 構文解析に特化した翻訳ソフト
- 大塚 寛 (愛媛大学理工学研究科) TRDRDに基づくサッカーの分析ソフトウェア
- Omar Rifki (Economic engineering department of Kyushu University) j Port Rob, Get Assets Data Set
- 吉野 聖人 (松江工業高等専門学校 電子制御工学科) ラプラシアン固有マップ法における評価方法及びその応用
- 田中 久治 (佐賀大学大学院工学系研究科) Coq Modules for Automata and Sticker Systems
- Sang-Hyup Seo(Department of Mathematics,Pusan National University)THE MONOTONE CONVERGENCE OF NEWTON'S METHOD FOR DIFFERENTIABLE CONVEX MATRIX FUNCTIONS

### Abstract †

#### Shoichi Tsuchiya †

- Title: On Halin graphs and generalized Halin graphs
- Abstract:
A
*Halin graph*, defined by Halin, is a plane graph such that is a spanning tree of with no vertices of degree where and is a cycle whose vertex set is the set of leaves of . On the other hand,*generalized Halin graph*is a graph such that is a spanning tree of with no vertices of degree where and is a cycle whose vertex set is the set of leaves of . 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.

#### Shuya Chiba †

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

#### Masashi Shinohara †

- Title: On complementary Ramsey numbers
- Abstract: In this talk, we propose a new generalization of Ramsey numbers which seems to be untreated in the literature.Instead of requiring the existence of a monochromatic clique, we consider the existence of a clique which avoids one of the colors in an edge coloring.These numbers are called complementary Ramsey numbers, and we derive their basic properties.We also establish their connections to graph factorizations. This is a joint work with Akihiro Munemasa.

#### 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 . 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.

#### Jong Hyeon Seo †

- Title: The Convergence of Relaxed Functional Iterations for Solving Quadratic Matrix Equations with an -matrix
- Abstract:
In stochastic areas, to find a special solution of a
*quadratic matrix equation*(QME) under probabilistic constraints is one of important issues. In this paper, first, we show the monotonic convergence of the*successive approximation method*(SAM) to the minimal nonnegative solution of QME under nonnegativity constraints which cover two different types of QMEs from probabilistic contexts, and explain theoretically why the SAM is always faster than the*fixed point iterative method*(FIM) in numerical experimentations. Second, we present a relaxed SAM which also preserves the monotonic convergence to the solution. Finally numerical experimentations give the new method actually improves convergence rate and is effective.

#### 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).