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IM-extendable claw-free graphs. (English) Zbl 0948.05045

Summary: J. Yuan introduced the definition of IM-extendable graphs in [J. Graph Theory 28, No. 4, 203-213 (1998; Zbl 0919.05054)]. Let \(G\) be a claw-free graph with \(2n\) vertices. In this paper, we prove that if \(G\) satisfies one of the following conditions then it is IM-extendable. (1) The minimum degree of \(G\) is at least \(2[n/2]+ 1\); (2) \(G\) is locally 2-connected; (3) \(G\) is \(k\)-regular with \(k\geq n\). We also show that all these results are best possible.

MSC:

05C75 Structural characterization of families of graphs

Citations:

Zbl 0919.05054
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