On k-orthogonal factorizations in networks

¹ School of Public Management, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
² Oujiang College, Wenzhou University, Wenzhou, Zhejiang 325035, P.R. China

^* Corresponding author: wangsufangjust@163.com

Received: 12 April 2020
Accepted: 10 March 2021

Abstract

Let m, n, k, r and k_i (1 ≤i ≤ m) are positive integers such that 1 ≤n ≤ m and k₁ ≥ k₂ ≥⋯≥k_m ≥ (r + 1)k. Let G be a graph with vertex set V(G) and edge set E(G), and H₁, H₂,⋯,H_r be r vertex-disjoint nk-subgraphs of G. In this article, we demonstrate that a graph G with maximum degree at most has a set of n pairwise edge-disjoint factors of G such that F_i has maximum degree at most k_i for 1 ≤ i ≤ n and is k-orthogonal to every H_j for 1 ≤ j ≤ r.