Forbidden Subgraphs for Hamiltonicity of 3-Connected Claw-Free Graphs
β Scribed by Jun Fujisawa
- Book ID
- 112121126
- Publisher
- John Wiley and Sons
- Year
- 2012
- Tongue
- English
- Weight
- 572 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
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
## Abstract Let __cl__(__G__) denote RyjΓ‘Δek's closure of a clawβfree graph __G__. In this article, we prove the following result. Let __G__ be a 4βconnected clawβfree graph. Assume that __G__[__N__~__G__~(__T__)] is cyclically 3βconnected if __T__ is a maximal __K__~3~ in __G__ which is also maxim
A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of orderp 2 4, containing no induced subgraph isomorphic to K1,31 is Hamilton-connected if and only if G is 3connected.