## 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,
A revision and extension of results on 4-regular, 4-connected, claw-free graphs
✍ Scribed by Trevor J. Gionet Jr.; Erika L.C. King; Yixiao Sha
- Book ID
- 108112936
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 219 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0166-218X
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## Abstract Let __cl__(__G__) denote Ryjáček's closure of a claw‐free graph __G__. In this article, we prove the following result. Let __G__ be a 4‐connected claw‐free graph. Assume that __G__[__N__~__G__~(__T__)] is cyclically 3‐connected if __T__ is a maximal __K__~3~ in __G__ which is also maxim
## Abstract A claw is an induced subgraph isomorphic to K~1,3.~ The claw‐point is the point of degree 3 in a claw. A graph is called p‐claw‐free when no p‐cycle has a claw‐point on it. It is proved that for p ≥ 4, p‐claw‐free graphs containting at least one chordless p‐cycle are edge reconstructibl