2020/09/04 by Qinghou Zeng, Zeng, Qinghou, Chunlei Zu +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2009.02175
openalex publication_date 2020/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let G be a multigraph in which no quadrilaterals share edges with triangles and other quadrilaterals and let μG(v)=max\μG(u,v):u∈ V(G)∖\v\\, where μG(u,v) is the number of edges joining u and v in G. We show that for any two functions a,b:V(G)→ℕ∖\0,1\, if dG(v)≥ a(v)+b(v)+2μG(v)-3 for each v∈ V(G), then there is a partition (X,Y) of V(G) such that dX(x)≥ a(x) for each x∈ X and dY(y)≥ b(y) for each y∈ Y. This extends the related results due to Diwan [3], Liu and Xu [7] and Ma and Yang [10] on simple graphs to the multigraph setting.