Random Latin square graphs

Authors

  • Demetres Christofides,

    Corresponding author
    1. Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Malostranské Námêstí 25, 188 00 Prague, Czech Republic
    • Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Malostranské Námêstí 25, 188 00 Prague, Czech Republic
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    • Supported by Engineering and Physical Sciences Research Council, The Cambridge Commonwealth Trust, Department of Mathematics and Mathematical Statistics of Umeå University.

  • Klas Markstrom

    1. Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden
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    • Supported by The Royal Physiographic Society in Lund.


Abstract

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and several similarities and differences are pointed out. For many properties our results for the general case are as strong as the known results for random Cayley graphs and sometimes improve the previously best results for the Cayley case. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011

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