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* Hakata Workshop 2014 [#x015faae]
''～ Discrete Mathematics and its Applications～''
#br
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.
**Organizers [#xb11a6e1]
-[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
-Hayato Waki (Kyushu University),~
-Takafumi Shibuta (Kyushu University),~
-[[Tetsuji Taniguchi:http://researchmap.jp/tetsuzit-14/]] (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 [#l7bc435b]
-[[Laboratory of Advanced Software in Mathematics, Institute of Mathematics for Industry, Kyushu University:http://imi.kyushu-u.ac.jp/lasm/]]
-JSPS KAKENHI(Grant-in-Aid for Exploratory Research) Grant Number 25610034.
-JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.
**Date [#gd461eaa]
Saturday, February 8, 2014
**Location [#vcadf025]
-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:http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=%E7%A6%8F%E5%B2%A1%E5%B8%82%E5%8D%9A%E5%A4%9A%E5%8C%BA%E5%8D%9A%E5%A4%9A%E9%A7%85%E6%9D%B11%E4%B8%81%E7%9B%AE16-14&aq=&sll=33.590188,130.425417&sspn=0.012888,0.021157&ie=UTF8&hq=&hnear=%E6%97%A5%E6%9C%AC,+%E7%A6%8F%E5%B2%A1%E7%9C%8C%E7%A6%8F%E5%B2%A1%E5%B8%82%E5%8D%9A%E5%A4%9A%E5%8C%BA%E5%8D%9A%E5%A4%9A%E9%A7%85%E6%9D%B1%EF%BC%91%E4%B8%81%E7%9B%AE%EF%BC%91%EF%BC%96%E2%88%92%EF%BC%91%EF%BC%94&ll=33.591064,130.424795&spn=0.012887,0.021157&z=16]] )
**Program [#w1b0acb9]
||~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 >#mc167ae6]]|
|10:30--11:20| Shuya Chiba (Kumamoto University)| [[On the number of components of &mimetex(2);-factors in claw-free graphs>#x53c044b]]|
|12:40--14:50|>| [[Poster Session (Software in Mathematics Demonstration Track):http://imi.kyushu-u.ac.jp/lasm/conf2014/]]|
|12:40--14:50|>| [[Poster Session (Software in Mathematics Demonstration Track):http://imi.kyushu-u.ac.jp/lasm/conf2014/index_en.html]]|
|15:10--16:00| Michio Seto (Shimane University)|[[Graph homomorphisms and de Branges-Rovnyak theory>#oda7b3bf]]|
|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>#cef5f33d]]|
|17:50--18:00|>|Closing (Yoshihiro Mizoguchi)|
**List of [[Poster session speakers:http://imi.kyushu-u.ac.jp/lasm/conf2014/]] [#u5f968b3]
**List of [[Poster session speakers:http://imi.kyushu-u.ac.jp/lasm/conf2014/index_en.html]] [#u5f968b3]
**Abstract [#t8f9abfa]
***Shoichi Tsuchiya [#mc167ae6]
-Title: On Halin graphs and generalized Halin graphs
-Abstract:
A ''' Halin graph''', defined by Halin, is a plane graph &mimetex(H=T \cup C); such that &mimetex(T); is a spanning tree of &mimetex(H); with no vertices of degree &mimetex(2); where &mimetex(|T|\geq 4); and
&mimetex(C); is a cycle whose vertex set is the set of leaves of &mimetex(T);.
On the other hand, ''' generalized Halin graph''' is a graph &mimetex(H=T \cup C); such that &mimetex(T); is a spanning tree of &mimetex(H); with no vertices of degree &mimetex(2); where &mimetex(|T|\geq 4); and &mimetex(C); is a cycle whose vertex set is the set of leaves of &mimetex(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.
***Shuya Chiba [#x53c044b]
-Title: On the number of components of &mimetex(2);-factors in claw-free graphs
-Abstract:
We consider only finite graphs without loops.
A graph &mimetex(G); is said to be '''claw-free''' if &mimetex(G); has no induced subgraph isomorphic to &mimetex(K_{1, 3});
(here &mimetex(K_{1, 3}); denotes the complete bipartite graph with partite sets of cardinalities &mimetex(1); and &mimetex(3);, respectively).
A &mimetex(2);-'''factor''' of a graph &mimetex(G); is a spanning subgraph of &mimetex(G); in which every component is a cycle.
It is a well-known
conjecture that every &mimetex(4);-connected claw-free graph is Hamiltonian
due to Matthews and Sumner
[Hamiltonian results in &mimetex(K_{1,3});-free graphs,
'''J. Graph Theory''' ''8'' (1984) 139--146].
Since a Hamilton cycle is a &mimetex(2);-factor with one component,
there are many results on the upper bounds of the number of components in &mimetex(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 &mimetex(2);-factor and
the minimum degree of a graph.
***Michio Seto [#oda7b3bf]
-Title: Graph homomorphisms and de Branges-Rovnyak theory
-Abstract:
In 1960's, de Branges and Rovnyak developed a theory dealing with
Hilbert space embedding &mimetex(H_1);&mimetex(\rightarrow);&mimetex(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.
***Shun'ichi Yokoyama [#cef5f33d]
-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).
