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1-factorizing regular graphs of high degree - an improved bound. (English) Zbl 0675.05030
The authors improve their previous results concerning 1-factorization of regular graphs of even order. Let G be a regular graph of even order and degree d(G). In their paper “Regular graphs of high degree are 1- factorizable”, Proc. Lond. Math. Soc., III. Ser. 50, 193-206 (1985; Zbl 0561.05027) the authors proved that if d(G)\(\geq (6/7)| V(G)|\) the G has a 1-factorization. In this paper they improve the bound to d(G)\(\geq (\sqrt{7}-1)| V(G)|\) which is slightly better than (5/6)\(| V(G)|\).
Reviewer: A.Hartman

MSC:
05C15 Coloring of graphs and hypergraphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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