New Ore‐Type Conditions for H‐Linked Graphs
Michael J. Ferrara, Ronald J. Gould, Michael S. Jacobson, Florian Pfender, Jeffrey S. Powell, Thor Whalen · Journal of Graph Theory · 2011
Abstract For a fixed (multi)graph H, a graph G is H‐linked if any injection f: V(H)→V(G) can be extended to an H‐subdivision in G. The notion of an H ‐linked graph encompasses several familiar graph classes, including k‐linked, k‐ordered and k‐connected graphs. In this article, we give two sharp Ore‐type degree sum conditions that assure a graph G is H ‐linked for arbitrary H. These results extend and refine several previous results on H ‐linked, k‐linked, and k‐ordered graphs. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:69–77, 2012