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Hamilton cycles in claw-heavy graphs

โœ Scribed by Bing Chen; Shenggui Zhang; Shengning Qiao


Book ID
108114026
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
509 KB
Volume
309
Category
Article
ISSN
0012-365X

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## Abstract We show that if __G__ is a 4โ€connected clawโ€free graph in which every induced hourglass subgraph __S__ contains two nonโ€adjacent vertices with a common neighbor outside __S__, then __G__ is hamiltonian. This extends the fact that 4โ€connected clawโ€free, hourglassโ€free graphs are hamilton

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## UNIVERSIW OF WATERLOO ' The research reported here has been sponsored by the Canadian Commonwealth Association.

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Matthews and Sumner have proved in [12] that if G is a 2-connected claw-free graph of order n such that 6>~(n-2)/3, then G is hamiltonian. Li has shown that the bound for the minimum degree 6 can be reduced to n/4 under the additional condition that G is not in /7, where /7 is a class of graphs defi