[0, k _i]₁ ^m-Factorizations Orthogonal to a Subgraph

Abstract

Let G be a graph, k₁, ···, k_m be positive integers. If the edges of graph G can be decomposed 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.