Large classes of infinite k-cop-win graphs

While finite cop-win finite graphs possess a good structural characterization, none is known for infinite cop-win graphs. As evidence that such a characterization might not exist, we provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each infinite cardinal κ and each positive integer k, we construct 2κ nonisomorphic k-cop-win graphs satisfying additional properties such as vertex-transitivity, or having universal endomorphism monoid and automorphism group.

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Anthony Bonato, Gena Hahn, Claude Tardif
• Keywords: Infinite Cop-win Graphs, JGT 2010, Nonisomorphic K-cop-win Graphs, finite Cop Number