A RELATIONSHIP BETWEEN THOMASSEN'S CONJECTURE AND BONDY'S CONJECTURE

被引：1

作者：

Cada, Roman ^{[1
,2
,3
]}

Chiba, Shuya ^{[4
]}

Ozeki, Kenta ^{[5
,6
]}

Vrana, Pete ^{[1
,2
,3
]}

Yoshimoto, Kiyoshi ^{[7
]}

机构：

[1] Univ W Bohemia, Dept Math, Plzen 30614, Czech Republic

[2] Charles Univ Prague, Ctr Excellence, ITI Inst Theoret Comp Sci, Plzen 30614, Czech Republic

[3] NTIS, European Ctr Excellence, Plzen 30614, Czech Republic

[4] Kumamoto Univ, Dept Math & Engn, Kurokami, Kumamoto 8608555, Japan

[5] Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan

[6] JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

[7] Nihon Univ, Coll Sci & Technol, Dept Math, Tokyo 1018308, Japan

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2015年 / 29卷 / 01期

关键词：

Hamiltonian cycles; line graphs; Thomassen's conjecture; dominating cycles; Bondy's conjecture; LINE GRAPHS; SUBGRAPHS;

D O I：

10.1137/130937974

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1986, Thomassen posed the following conjecture: every 4-connected line graph has a Hamiltonian cycle. As a possible approach to the conjecture, many researchers have considered statements that are equivalent or related to it. One of them is the conjecture by Bondy: there exists a constant c(0) with 0 < c(0) <= 1 such that every cyclically 4-edge-connected cubic graph H has a cycle of length at least c(0)\V (H)\. It is known that Thomassen's conjecture implies Bondy's conjecture, but nothing about the converse has been shown. In this paper, we show that Bondy's conjecture implies a slightly weaker version of Thomassen's conjecture: every 4-connected line graph with minimum degree at least 5 has a Hamiltonian cycle.

引用

页码：26 / 35

页数：10

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