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The multiplicity of 1-factors in the square of a graph. (English) Zbl 0545.05050
It is known that the square of each connected graph of even order has a 1-factor. The author shows that the square of any connected graph of order 2n has at least n 1-factors. Moreover, all the extremal graphs are described; they turn out to be special trees.
Reviewer: J.Širáň

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C35 Extremal problems in graph theory
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References:
[1] , and , Graphs and Digraphs. Prindle, Weber and Schmidt, Boston (1979).
[2] Chartrand, Indag. Math. 35 pp 228– (1973)
[3] Nebesk, J. Graph Theory 2 pp 251– (1978)
[4] Sumner, Proc. Amer. Math. Soc. 42 pp 8– (1974)
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