Counting 1-factors in infinite graphs

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Abstract

F. Bry (J. Combin. Theory Ser. B 34 (1983), 48–57) proved that a locally finite infinite n-connected factorizable graph has at least (n−1)! 1-factors and showed that for n = 2 this lower bound is sharp. We prove that for n≥3 any infinite n-connected factorizable graph has at least n! 1-factors (which is a sharp lower bound).

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