2022/05/19 by Morteza Hasanvand, Hasanvand, Morteza
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2205.09715
openalex publication_date 2022/05/19 · 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)→ Zk be a mapping with ∑v∈ Xf(v) \stackrelk≡∑v∈ Yf(v). In this paper, we show that if G is (2m+2m0+4k-4)-edge-connected and m+m0>0, then G has an m-tree-connected factor H such that its complement is m0-tree-connected and for each vertex v, dH(v)\stackrelk≡ f(v), and \lfloor(dG(v))/(2)\rfloor-(k-1)-m0≤ dH(v)≤ \lceil(dG(v))/(2)\rceil+k-1+m. Next, we generalize this result to general graphs and derive a sufficient degree condition for a highly edge-connected general graph G to have a connected factor H such that for each vertex v, dH(v)∈ \f(v),f(v)+k\. Finally, we show that every (4k-2)-tree-connected graph admits a bipartite connected factor whose degrees are divisible by k.