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Factors of claw-free graphs. (English) Zbl 0794.05106
Recently, many papers have been concerned with the properties of claw- free graphs. In the present paper we follow up with the study of factors of the claw-free graphs which originated from the following well-known result by D. P. Sumner [Proc. Am. Math. Soc. 42, 8-12 (1974; Zbl 0293.05157)].
Theorem. Every connected claw-free graph having an even number of vertices has a perfect matching.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
##### Keywords:
claw-free graphs; factors; perfect matching
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##### References:
 [1] Favaron O., Lonc Z., Truszcyński M.: Decompositions of Graphs into Graphs with Three Edges. Ars Combinatoria 20 (1985), 125-146. · Zbl 0604.05028 [2] Harary F.: Graph Theory. Addison-Wesley, Reading 1969. · Zbl 0196.27202 [3] Lovász L., Plummer M. D.: Matching Theory. Akadémiai Kiadó, Budapest 1986. · Zbl 0618.05001 [4] Ryjáček Z.: Factors and Circuits in $$K_ {1,3}$$-free Graphs. Combinatorics and Graph Theory, Banach Center Publications, Vol. 25, PWN, Warsaw 1989. · Zbl 0727.05047 [5] Sumner D. P.: Graphs with l-factors. Proc. Amer. Math. Soc. 42 (1974), 8-12. · Zbl 0293.05157
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