Quadrangularly connected claw-free graphs
type: Item
instance of: scholarly article
title: Quadrangularly connected claw-free graphs
zbMATH Open document ID: 1118.05057
author: Cheng Guo
author: Dengxin Li
author: Hong-Jian Lai
author: Mingchu Li
author: Liming Xiong
published in: Discrete Mathematics
publication date: 2007-03-15T00:00:00Z
review text: Let \(G_1\) be a graph arising from the cycle \(C_8\) with vertices \(x_1,x_2,\dots ,x_8\) by adding the edges of the cycle \(C_4\) with vertices \(x_1,x_3,x_5,x_7\) and let \(G_2\) be the graph obtained from \(G_1\) by adding the edge \(x_1x_5\). Let \(N(v,G)\) be the subgraph of a graph \(G\) induced by the set of all vertices adjacent to the vertex \(v\). \(G\) is quadrangularly connected if for every two edges \(e_1,e_2\) of \(G\) there is a sequence of cycles of length 3 or 4, \(C_1,C_2,\dots,C_r\), such that \(e_1\in E(C_1), e_2\in E(C_r)\) and \(E(C_i)\cap E(C_{i+1})\neq\emptyset\) for \(i=1,2,\dots,r-1\). It is shown that if \(G\) is a quadrangularly connected claw-free graph, which does not contain \(G_1\) or \(G_2\) as an induced subgraph and \(N(v,G)\) is disconnected for every vertex \(v\) of degree 4, then \(G\) is Hamiltonian.
reviewed by: Dalibor Fronček
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 5134189
zbMATH Keywords: claw-free graphs
zbMATH Keywords: quadrangular connectivity
MaRDI profile type: Publication
full work available at URL: j.disc.2006.07.034
OpenAlex ID: W2079821081
cites work: Q5422499
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DOI: 10.1016/J.DISC.2006.07.034
description: scientific article; zbMATH DE number 5134189