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Bounded Degree, Triangle Avoidance Graph Games

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Abstract

We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on n vertices. The two players take turns choosing edges within K n , building up a simple graph. The edges must be chosen according to a set of restrictions \({\mathcal{R}}\) . The winner is the last player to choose an edge that does not violate any of the restrictions in \({\mathcal{R}}\) . For fixed n and \({\mathcal{R}}\) , one of the players has a winning strategy. For various games where \({\mathcal{R}}\) includes bounded degree and triangle avoidance, we determine the winner for all values of n.

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Authors and Affiliations

  1. The Ohio State University, Columbus, USA

    Nishali Mehta & Ákos Seress

  2. Centre for Mathematics of Symmetry and Computation, University of Western Australia, Crawley, Australia

    Ákos Seress

Authors
  1. Nishali Mehta
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  2. Ákos Seress
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Correspondence to Nishali Mehta.

Additional information

Research partially supported by the NSF and by ARC Grant DP1096525.

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Mehta, N., Seress, Á. Bounded Degree, Triangle Avoidance Graph Games. Graphs and Combinatorics 29, 637–660 (2013). https://doi.org/10.1007/s00373-011-1121-3

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  • DOI: https://doi.org/10.1007/s00373-011-1121-3

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