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Claw-free graphs are not universal fixers

✍ Scribed by E.J. Cockayne; R.G. Gibson; C.M. Mynhardt

Book ID
108113986
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
437 KB
Volume
309
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

Claw-free graphs are edge reconstructibl
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The Edge Reconstruction Conjecture states that all graphs with at least four edges are determined by their edge-deleted subgraphs. We prove that this is true for claw-free graphs, those graphs with no induced subgraph isomorphic to K,,3. This includes line graphs as a special case.

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## Abstract We show that every 3‐connected claw‐free graph which contains no induced copy of __P__~11~ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of __P__~12~ this result is, in a way, best possible. Β© 2004 Wiley Periodicals, Inc. J Graph T

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A graph is Hamilton-connected if any pair of vertices is joined by a hamiltonian path. In this note it is shown that 9-connected graphs which contain no induced claw K 1, 3 are Hamilton-connected, by reformulating and localizing a closure concept due to Ryja c ek, which turns claw-free graphs into l

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Thomassen conjectured that every 4-connected line graph is hamiltonian. Here we shall see that 4-connected line graphs of claw free graphs are hamiltonian connected.