Hamilton cycles in 1-tough triangle-free graphs

A graph G is called triangle-free if G has no induced K 3 as a subgraph. We set σ 3= min{∑ i=1 3 d(v i)|{v 1,v 2,v 3} is an independent set of vertices in G}. In this paper, we show that if G is a 1-tough and triangle-free graph of order n with n⩽ σ 3, then G is hamiltonian.

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Bibliographic Details
Published inDiscrete mathematics Vol. 254; no. 1; pp. 275 - 287
Main Authors Li, Xiangwen, Wei, Bing, Yu, Zhengguang, Zhu, Yongjin
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 10.06.2002
Elsevier
Subjects
1-tough
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Hamiltonian graph
Mathematics
Sciences and techniques of general use
Triangle-free
Triangle-free
1-tough
Hamiltonian graph
Subgraph
Vertex(graph)
Cycle(graph)
Finite graph
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Summary:A graph G is called triangle-free if G has no induced K 3 as a subgraph. We set σ 3= min{∑ i=1 3 d(v i)|{v 1,v 2,v 3} is an independent set of vertices in G}. In this paper, we show that if G is a 1-tough and triangle-free graph of order n with n⩽ σ 3, then G is hamiltonian.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(01)00358-2