Ore-type degree conditions for a graph to be H-linked

Given a fixed multigraph H with V (H) = {h1, . . . , hm}, we say that a graph G is H-linked if for every choice of m vertices v1, . . . , vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing hi for every i. This generalizes the notion of k-linked graphs (as well as some other notions). For a family H of graphs, a graph G is H-linked if G is H-linked for every H H. In this paper we estimate the minimum integer r = r(n, k, d) such that each n-vertex graph with 2(G) r is H-linked, where H is the family of simple graphs with k edges and minimum degree at least d 2.

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Alexandr V. Kostochka, Gexin Yu
• Keywords: Branch Vertex, JGT 2008, K-linked Graphs, Multigraph