2017 Fiscal Year Final Research Report
On Thomassen Conjecture and Tutte closed trail Problem
Project/Area Number |
26400190
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Foundations of mathematics/Applied mathematics
|
Research Institution | Nihon University |
Principal Investigator |
|
Research Collaborator |
OZEKI Kenta
CHIBA Shyuya
RYJACEK Zdenek
CADA Roman
LI Hao
DU Hui
FAUDREE Ralph
SCHELP Richard
VRANA Peter
LEHEL Jeno
HULGAN Jonathan
XIONG Liming
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Keywords | ハミルトンサイクル / 2因子 / Thomassen予想 / Bondy予想 / Tutte閉トレイル / cubicグラフ |
Outline of Final Research Achievements |
Thomassen's conjecture is that any 4-edge connected line graph has a Hamilton cycle. This conjecture is equivalent to the following conjecture: any essentially 4-edge connected graph has a edge dominating cycle. In this research, we mainly studied followings: 1. existence of 2-factors in 4-edge connected line graphs which has properties weaker than properties of Hamilton cycles and 2. existence of Tutte closed trails in any essentially 4-edge connected graph. In consequence, we obtained followings: 1. the relation and the equivalence on Thomassen's conjecture and Bondy's conjecture and 2. in essentially 3-edge connected cubic graphs, the existence and the number of connected components of spanning subgraphs in which every connected components are closed trails. Such spanning subgraphs generalizes 2-factors. The third result improve the results by Yoshimoto and Bill Jackson on the number of connected components of essentially 3-edge connected cubic graphs.
|
Free Research Field |
グラフ理論
|