A degree condition for the existence of k-factors

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Abstract

Let k be an integer such that ≦, and let G be a connected graph of order n with ≦, kn even, and minimum degree at least k. We prove that if G satisfies max(deg(u), deg(v)) ≦ n/2 for each pair of nonadjacent vertices u, v in G, then G has a k-factor.

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