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 for every i, vi is the branch vertex representing hi. This generalizes the notion of k-linked graphs (as well as some other notions). For a family ${\cal H}$ of graphs, a graph G is ${\cal H}$-linked if G is H-linked for every $H\in {\cal H}$. In this article, we estimate the minimum integer r = r(n, k, d) such that each n-vertex graph with $\sigma_{2}(G)\ge {r}$ is ${\cal H}$-linked, where ${\cal H}$ is the family of simple graphs with k edges and minimum degree at least $d \ge 2$. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 1426, 2008
['Alexandr V. Kostochka', 'Gexin Yu']
Ore-type degree conditions for a graph to be H-linked