Unavoidable topological minors of infinite graphs

A graph G is loosely-c-connected, or -c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of -c-connected infinite graphs that form an unavoidable set among the topological minors of -c-connected infinite graphs. Corresponding results for minors and parallel minors are also obtained.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Carolyn Chun, Guoli Ding
• Keywords: DM 2010, Infinite, Infinite Component, Infinite Graphs