科研之友
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摘要
Let G be a connected simple graph, and let f be a mapping from V(G) to the set of integers. This paper is concerned with the existence of a spanning tree in which each vertex v has degree at least f(v). We show that if |G(S)|-f(S)+|S|1 for any nonempty subset SL, then a connected graph G has a spanning tree such that dT(x)f(x) for all xV(G), where G(S) is the set of neighbors v of vertices in S with v?S, L={xV(G):f(x)2}, and dT(x) is the degree of x in T. This is an improvement of several results, and the condition is best possible.
- 出版日期2015-7
