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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
Citations:
Zbl 0536.05047
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References:
[1] and , Graph Theory with Applications, Macmillan Press, London, (1976). · Zbl 1226.05083
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[7] Zhang, J. Graph Theory 12 pp 209– (1988)
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