关于图的(g,f)-因子分解
On(g, f)-Factorizations of Graghs
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摘要: 设G是一个图,g和f是定义在图G的顶点集V(G)上的两个非负整数值函数且g<f.图G的一个(g,f)-因子是G的一个支撑子图F,使对所有的x∈V(G)有g(x)≤dF(x)≤f(x).若G本身是一个(g,f)-因子,则称G是一个(g,f)-图.若G的边能分解成一些边不交的(g,f)-因子,则称G是(g,f)-因子可分解的.本文给出图G是(g,f)-因子可分解的一个充分条件.Abstract: Let G be a graph and g, f be two nonnegative integer-valued functions defined on thevertices set V(G) of G and g≤f, A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)≤dF(x)≤f(x) for all x∈V(G). If G itself is a (g, f)-factor, then itis said that G is a (g, f)-graph. If the edges of G can be decomposed into some edgedisjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, onesufficient condition for a graph to be (g, f)-factorable is given.
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Key words:
- graph /
- factor /
- factorization
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