与任意图正交的[0, ki]1m-因子分解

与任意图正交的[0, k_i]₁^m-因子分解

基金项目: 国家自然科学基金资助项目(69971018)

1.
Electronic Engineering Research Institute, Xidian University, Xi'an 710071, P R China;
2.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P R China

摘要: 设G是一个图,k₁,…,k_m是正整数。若图G的边能分解成m个边不交的 [0,k₁]-因子F₁,…,[0,k_m]-因子F_m,则称F={F₁,…,F_m}是G的一个[0,k_i]₁^m-因子分解。如果H是G的一个有m条边的子图且对任意的 1≤i≤m有|E(H)∩E(F_i)|=1,则称 F与H正交。证明了若G是一个 [0,k₁+… +k_m-m+1]-图,H是G的一个有m条边的子图,则图G有一个[0,k_i]₁^m-因子分解与H正交。
- 图 /
- 因子 /
- 因子分解 /
- 正交因子分解
Abstract: Let G be a graph,k₁,…,k_m be positive integers.If the edges of graph G can be decom- posed into some edge disjoint [0,k₁]-factor F₁…,[0,k_m]-factor F_m then we can say F={F₁,…,F_m},is a [0,k_i]₁^m-factorization of G.If H is a subgraph with m edges in graph G and |E(H)∩E(F_i)|=1 for all 1≤i≤m,then we can call that F is orthogonal to H.It is proved that if G is a[0,k₁+… +k_m-m+1]-graph,H is a subgraph with m edges in G,then graph G has a [0,k_i]₁^m-factorization orthogonal to H.
- graph /
- factor /
- factorization /
- orthogonal factorization

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