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Hamiltonian cycles and 2-dominating induced cycles in claw-free graphs

✍ Scribed by Jinfeng Feng


Publisher
Springer
Year
2008
Tongue
English
Weight
186 KB
Volume
69
Category
Article
ISSN
0340-9422

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Hamiltonian cycles in 2-connected claw-f
✍ Hao Li πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 418 KB πŸ‘ 2 views

## Abstract M. Matthews and D. Sumner have proved that of __G__ is a 2‐connected claw‐free graph of order __n__ such that Ξ΄ ≧ (__n__ βˆ’ 2)/3, then __G__ is hamiltonian. We prove that the bound for the minimum degree Ξ΄ can be reduced to __n__/4 under the additional condition that __G__ is not in __F_

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## Abstract In this paper, we show that every 3‐connected claw‐free graph on n vertices with Ξ΄ β‰₯ (__n__ + 5)/5 is hamiltonian. Β© 1993 John Wiley & Sons, Inc.

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Flandrin et ai. (to appear) define a simple bipartite graph to be biclaw-free if it contains no induced subgraph isomorphic to H, where H could be obtained from two copies of K1.3 by adding an edge joining the two vertices of degree 3. They have shown that if G is a bipartite, balanced, biclaw-free