关于特殊[a,b]-因子的度条件

THE DEGREE CONDITIONS FOR A GRAPH TO HAVE SPECIAL[a,b]-FACTORS

设G=(V(G),E(G))是一个图,1≤a≤b是整数。G的一个支撑子图F称为G的一个[a,b]-因子,若对G中任意的点v∈V(G),有a≤dF(v)≤b.图G称为是[a,b]-覆盖图,若对G的每一条边,存在G的一个[a,b]-因子包含它。本文给出了一个图是[a,b]-覆盖图的度条件,推广了T.Nishimura等人得到的结果。

Let c be a graph with vertices set v（G） and edge set E（G） ,a and b be integers such that 1 ≤a≤b. A spanning subgraph F of G is called an [ a, b ] - factor of G, if a ≤ dp （v）≤ b for each v ∈ V（G）. G is called [ a, b ] - covered graph if for each edge e ∈ V（G） there is an [ a, b] - factor of G containing it. A degree condition for G be an [ a, b] - covered graph is given, as a generalization of T. Nishimura＇s theorem. Key Words： [ a, b ] - factor; [ a, b ] - covered graph ; degree