## Abstract There are many results concerned with the hamiltonicity of __K__~1,3~‐free graphs. In the paper we show that one of the sufficient conditions for the __K__~1,3~‐free graph to be Hamiltonian can be improved using the concept of second‐type vertex neighborhood. The paper is concluded with
Connected, locally 2-connected, K1,3-free graphs are panconnected
✍ Scribed by S. V. Kanetkar; P. R. Rao
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 288 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
A graph G is locally n‐connected, n ≥ 1, if the subgraph induced by the neighborhood of each vertex is n‐connected. We prove that every connected, locally 2‐connected graph containing no induced subgraph isomorphic to K~1,3~ is panconnected.
📜 SIMILAR VOLUMES
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We prove the following conjecture of Broersma and Veldman: A connected, locally k-connected K,,-free graph is k-hamiltonian if and only if it is (k + 2)-connected ( k L 1). We use [ 11 for basic terminology and notation, and consider simple graphs only. Let G be a graph. By V(G) and E(G) we denote,
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## Abstract We show that every 3‐connected claw‐free graph which contains no induced copy of __P__~11~ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of __P__~12~ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph T
## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2‐connected claw‐free graph of order __n__ such that δ ≧ (__n__ − 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree δ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_