Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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,  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,  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
['Anthony Bonato', 'Geňa Hahn', 'Claude Tardif']
I am writing a research paper on a idea Large classes of infinite k-cop-win graphs
[{"from": "human", "value": "I am writing a research paper on a idea Large classes of infinite k-cop-win graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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,  provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each infinite cardinal \u03ba and each positive integer k,  construct 2\u03ba non-isomorphic k-cop-win graphs satisfying additional properties such as vertex-transitivity, or having universal endomorphism monoid and automorphism group. \u00a9 2010 Wiley Periodicals, Inc. J Graph Theory 65: 334\u2013342, 2010"}]