A generalization of Stiebitz-type results on graph decomposition

Abstract

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 µis the number of edges joining u and v in G. We show that for any two functions a, b :for each x ∈ X and d Y (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.