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Hamiltonian cycles in 2-connected claw-free-graphs. (English) Zbl 0841.05062
M. Matthews and D. P. Sumner [J. Graph Theory 8, 139-146 (1984; Zbl 0536.05047)] proved that a 2-connected claw-free graph of order $$n$$ is Hamiltonian provided that its minimum degree $$\delta$$ is at least $$(n- 2)/3$$. In the paper under review, it is shown that the above minimum degree requirement can be relaxed to $$n/4$$ if the graph $$G$$ satisfies a certain type of indecomposability condition.

##### MSC:
 05C45 Eulerian and Hamiltonian graphs 05C35 Extremal problems in graph theory 05C38 Paths and cycles
##### Keywords:
Hamiltonian graphs; claw-free graph; indecomposability
Zbl 0536.05047
Full Text:
##### References:
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