REGARDING r-ORTHOGONAL FACTORIZATIONS IN BIPARTITE GRAPHS
Sizhong Zhou · Rocky Mountain Journal of Mathematics · 2025
Let m, t, r and ki (1≤i≤m) be positive integers with ki≥(2r−1)t+1. Let G be a graph, H be an mr-subgraph of G, and ℱ={F1,F2,…,Fm} be a (g,f)-factorization of G. If for any partition {A1,A2,…,Am} of E(H) with |Ai|=r, G has a (g,f)-factorization ℱ={F1,F2,…,Fm} with Ai⊆E(Fi), 1≤i≤m, then we say that G has (g,f)-factorizations randomly r-orthogonal to H. Let H1,H2,…,Ht be t vertex-disjoint mr-subgraphs of a bipartite graph G with Δ(G)≤k1+k2+⋯+km−m+1. We demonstrate that a bipartite graph G with Δ(G)≤k1+k2+⋯+km−m+1 possesses a [0,ki]1m-factorization randomly r-orthogonal to every Hi, 1≤i≤t.