科研之友
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摘要
Let G be a graph of order n. Let a and b be integers with 1 <= a <= b, and let k >= 2 be a positive integer not larger than the independence number of G. Let g(x) and f(x) be two nonnegative integer-valued functions defined on V(G) such that a <= g(x) < f(x) <= b for each x is an element of V(G). Then G has a (g, f)-factor if the minimum degree delta(G) >= b(b-1)(k-1)/a+1, n > (a+b)(k(a+b)-2)/a+1 and vertical bar N(G)(x(1)) boolean OR N(G)(x(2)) boolean OR ... U NG(x(k))vertical bar >= (b-1)n/a+1 for any independent subset {x(1), x(2),..., x(k)} of V(G). Furthermore, we show that the result is best possible in some sense.
