与任意图(m,r)-正交的(g,f)-因子分解  

(g.f)-Factorizations (m,r)-Orthogonal to an Arbitrary Graph

作　　者：桂国祥[1] 刘展鸿[1] 

机构地区：[1]江西师范大学数信学院,江西南昌330027

出　　处：《华东交通大学学报》2005年第1期149-151,共3页Journal of East China Jiaotong University

摘　　要：设G是一个图,用V(G)和E(G)表示它的顶点集和边集,并设g(x)和f(x)是定义在V(G)上的两个整数值函数,且对每个x∈V(G),有52r-1≤g(x)≤f(x),则图G的一个支撑子图F称为G的一个(g,f)-因子,如果对每个x∈V(G),有g(x)≤dF(x)≤f(x).图G的(g,f)-因子分解是指E(G)能划分成边不交的(g,f)-因子,设F={F1,F2,…,Fm}和H分别是图G的因子分解和子图,若对所有1≤i≤m有|E(H)∩E(Fi)|=r,则称F和H(m,r)-正交.本文证明:若G是一个(mg+m-1,mf-m+1)-图,H是G中任一有mr条边的子图,则G有一个(g,f)-因子分解与H(m,r)-正交.Let G be a graph with vertex set V(G) and edge set E(G), and Let g(x) and f(x) be two integer-valued functions defined on V(G) such as 52r-1≤g(x)≤f(x) for every x∈V(G). Then a (g,f)-factor of G is a spanning subgraph F of G such as g(x)≤dF(x)≤f(x) for every x∈V(G). The (g,f)-factorization of G is a partition of E(G) into edge-disjoint (g,f)-factors. Let F={F1,F2,…,Fm} and H be the factorization and a subgraph of G, respectively. If Fi ,1≤i≤m, has exactly r edges in common with H, then it is said that F is (m,r)-orthogonal to H. This paper proves that for any mr-subgraph H of an (mg+m-1,mf-m+1)-graph G , there exists a (g,f)-factorization (m,r)-orthogonal to H

关 键 词：(G F)-因子分解 支撑子图 正交 边集 顶点集 整数值函数 表示 意图 划分 

分 类 号：U469.1[机械工程—车辆工程] O157.5[交通运输工程—载运工具运用工程]