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Tank-Ring Factors in Supereulerian Claw-Free Graphs

✍ Scribed by MingChu Li, Lifeng Yuan, He Jiang, Bing Liu, H. J. Broersma


Book ID
120788670
Publisher
Springer Japan
Year
2011
Tongue
English
Weight
255 KB
Volume
29
Category
Article
ISSN
0911-0119

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## Abstract We consider the existence of several different kinds of factors in 4‐connected claw‐free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4‐connected line graph is hamiltonian,

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A graph is said to be claw-free if it does not contain an induced subgraph isomorphic to KI,3. Let k be a positive integer. Our main result is as follows: If G is a claw-free graph of order at least 3k and d(x) + d(y)>~3k + 1 for every pair of non-adjacent vertices x and y of G, then G contains k v