Large classes of infinite  k ‐cop‐win graphs | Zendy

Bonato Anthony | Zendy; Hahn Geňa | Zendy; Tardif Claude | Zendy

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Large classes of infinite k ‐cop‐win graphs

Author(s) -

Bonato Anthony,

Hahn Geňa,

Tardif Claude

Publication year - 2010

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20484

Subject(s) - mathematics , combinatorics , automorphism , vertex (graph theory) , discrete mathematics , characterization (materials science) , endomorphism , graph , transitive relation , cograph , 1 planar graph , chordal graph , materials science , nanotechnology

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 2 κ 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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