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On a Closure Concept in Claw-Free Graphs

✍ Scribed by Zdeněk Ryjáček

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
269 KB
Volume
70
Category
Article
ISSN
0095-8956

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✦ Synopsis

If G is a claw-free graph, then there is a graph cl(G) such that (i) G is a spanning subgraph of cl(G), (ii) cl(G) is a line graph of a triangle-free graph, and (iii) the length of a longest cycle in G and in cl(G) is the same.

A sufficient condition for hamiltonicity in claw-free graphs, the equivalence of some conjectures on hamiltonicity in 2-tough graphs and the hamiltonicity of 7-connected claw-free graphs are obtained as corollaries.

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