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Operations Research Transactions >

2016 , Vol. 20 >Issue 1: 112 - 117

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.011

The Hamilton-connectivity with the degree sum of  non-adjacent subgraphs P_ 4 and K_1 in claw-free graphs

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  • 1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710072, China

Received date: 2015-01-19

  Online published: 2016-03-15

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Abstract

This paper studies the relationship between the degree of subgraphs and Hamiltonicity of graphs. It is proven that every 3-connected claw-free graph $G$ of order $n$ with minimum degree $\delta(G)\geq4$ is Hamilton-connected if it satisfies $d(H_1)+d(H_2)\geq n$ for any two non-adjacent subgraphs $H_1$, $H_2$ which are isomorphic to $P_4$, $K_1$ respectively.

Key words：  claw-free graph; non-adjacent subgraph; degree of subgraph; Hamilton-connected

Cite this article

ZHENG Wei, WANG Ligong . The Hamilton-connectivity with the degree sum of  non-adjacent subgraphs P_ 4 and K_1 in claw-free graphs[J]. Operations Research Transactions, 2016 , 20(1) : 112 -117 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.011

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