We show that, in a claw-free graph, Hamilton-connectedness is preserved under the operation of local completion performed at a vertex with 2-connected neighborhood. This result proves a conjecture by Bollobás et al.
Closure, clique covering and degree conditions for Hamilton-connectedness in claw-free graphs
✍ Scribed by Roman Kužel; Zdeněk Ryjáček; Jakub Teska; Petr Vrána
- Book ID
- 113567626
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 729 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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Using Ryja c ek's closure, we prove that any 3-connected claw-free graph of order & and minimum degree $ &+38 10 is hamiltonian. This improves a theorem of Kuipers and Veldman who got the same result with the stronger hypotheses $ &+29 8 and & sufficiently large and nearly proves their conjecture sa
In this article, we study cycle coverings and 2-factors of a claw-free graph and those of its closure, which has been defined by the first author (On a closure concept in claw-free graphs, J Combin Theory Ser B 70 (1997), 217-224). For a claw-free graph G and its closure cl(G), we prove: ( 1 (2) G