2022/05/18 by Morteza Hasanvand, Hasanvand, Morteza · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2205.09012
openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a bipartite graph with bipartition (X,Y), let k be a positive integer, and let f:V(G)→ \-1,…, k-2\ be a mapping with ∑v∈ Xf(v) \stackrelk≡∑v∈ Yf(v). In this paper, we show that if G is essentially (3k-3)-edge-connected and for each vertex v, dG(v)≥ 2k-1+f(v), then it admits a factor H such that for each vertex v, dH(v)\stackrelk≡ f(v), and \lfloor(dG(v))/(2)\rfloor-(k-1)≤ dH(v)≤ \lceil(dG(v))/(2)\rceil+k-1. Next, we generalize this result to general graphs and derive sufficient conditions for a highly edge-connected general graph G to have a factor H such that for each vertex v, dH(v)∈ \f(v),f(v)+k\. Finally, we show that every (4k-1)-edge-connected essentially (6k-7)-edge-connected graph admits a bipartite factor whose degrees are positive and divisible by k.