摘要
Simple graphs are considered. Let \%G\% be a graph and \%g(x)\% and \%f(x)\% integer\|valued functions defined on \%V(G)\% with \%g(x)≤f(x)\% for every x∈V(G) . For a subgraph \%H\% of \%G\% and a factorization F={F 1,F 2, ...,F t} of \%G\%, if | E(H)∩E(F i)|=1, 1≤i≤t , then we say that F is orthogonal to \%H\%. It is proved that for an \%(mg(x)+k, mf(x)-k)\% graph \%G\%, there exists a subgraph \%R\% of \%G\% such that for any subgraph \%H\% of \%G\% with | E(H)|=k, \%R\% has a \%(g,f)\%\|factorization orthogonal to \%H\%, where \%1≤k<m\% and \%g(x)≥1\% or \%f(x)≥5\% for every x∈V(G).
Simple graphs are considered. Let G be a graph andg(x) andf(x) integer-valued functions defined on V(G) withg(x)?f(x) for everyx?V(G). For a subgraphH ofG and a factorizationF=|F 1,F 2,?,F 1| ofG, if |E(H)∩E(F 1)|=1,1?i?j, then we say thatF orthogonal toH. It is proved that for an (mg(x)+k,mf(x) -k)-graphG, there exists a subgraphR ofG such that for any subgraphH ofG with |E(H)|=k,R has a (g,f)-factorization orthogonal toH, where 1?k<m andg(x)?1 orf(x)?5 for everyx?V(G).
基金
ProjectsupportedbytheChinaPostdoctoralScienceFoundation
ChuangXinFoundationoftheChineseAcademyofSci ences.
