The existence of subdigraphs with orthogonal factorizations in digraphs

Abstract

Let $G$ be a $[0,k_1+k_2+\cdots+k_m-n+1]$-digraph and $H_1,H_2,\cdots,H_r$ be $r$ vertex-disjoint $n$-subdigraphs of $G$, where $m,n,r$ and $k_i$ ($1\leq i\leq m$) are positive integers satisfying $1\leq n\leq m$ and $k_1\geq k_2\geq\cdots\geq k_m\geq r+1$. In this article, we verify that there exists a subdigraph $R$ of $G$ such that $R$ possesses a $[0,k_i]_1^{n}$-factorization orthogonal to every $H_i$ for $1\leq i\leq r$.

Keywords

• network
• digraph
• subdigraph
• factor
• orthogonal factorization