Degree conditions and fractional k-factors of graphs
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Let k≥1 be an integer, and let G be a 2-connected graph of order n≥,max{7, 4k+1}, and the minimum degree δ(G)≥ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{d_G(x),d_G(y)}≥n/2 for each pair of nonadjacent vertices x,y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.
Abstract
Let k≥1 be an integer, and let G be a 2-connected graph of order n≥,max{7, 4k+1}, and the minimum degree δ(G)≥ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{d_G(x),d_G(y)}≥n/2 for each pair of nonadjacent vertices x,y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.
참고문헌 (13)
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