Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4650474 | Discrete Mathematics | 2008 | 5 Pages |
Abstract
Let G be a graph. For u,v∈V(G)u,v∈V(G) with distG(u,v)=2distG(u,v)=2, denote JG(u,v)={w∈NG(u)∩NG(v)|NG(w)⊆NG(u)∪NG(v)∪{u,v}}JG(u,v)={w∈NG(u)∩NG(v)|NG(w)⊆NG(u)∪NG(v)∪{u,v}}. A graph G is called quasi claw-free if JG(u,v)≠∅JG(u,v)≠∅ for any u,v∈V(G)u,v∈V(G) with distG(u,v)=2distG(u,v)=2. In 1986, Thomassen conjectured that every 4-connected line graph is hamiltonian. In this paper we show that every 4-connected line graph of a quasi claw-free graph is hamiltonian connected.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hong-Jian Lai, Yehong Shao, Mingquan Zhan,