Abstract

AbstractWhile 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 non‐isomorphic k‐cop‐win graphs satisfying additional properties such as vertex‐transitivity, or having universal endomorphism monoid and automorphism group. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 334–342, 2010

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