Tank-Ring Factors in Supereulerian Claw-Free Graphs
β 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 4βconnected clawβfree 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 4βconnected line graph is hamiltonian,
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