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SHUTOUT GAMES ON GRAPHS

Part of: Graph theory Game theory

Published online by Cambridge University Press:  03 February 2015

Alexandru Cioba  and
Michail Savvas
Alexandru Cioba
Affiliation:
Department of Mathematics, University College London, 25 Gordon Street, London WC1H 0AY, U.K. email [email protected]
Michail Savvas
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford 94305-2125, U.S.A. email [email protected]
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Abstract

Two players take it in turn to claim edges from a graph $G$. The first player (“Maker”) wins if at any point he has claimed $s$ edges at a vertex without the second player (“Breaker”) having claimed a single edge at that vertex. If, by the end of play, this does not occur we say that Breaker wins. Our main aim is to show that for every $s$ there is a graph $G$ in which Maker has a winning strategy.

MSC classification

Primary: 91A43: Games involving graphs 91A46: Combinatorial games 05C57: Games on graphs
Type
Research Article
Information
Mathematika , Volume 61 , Issue 3 , September 2015 , pp. 523 - 530
Copyright
Copyright © University College London 2015 

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References

Beck, J., Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and Its Applications 114), Cambridge University Press (Cambridge, 2008).CrossRefGoogle Scholar
Leader, I., Hypergraph Games. Notes available online at http://tartarus.org/gareth/maths/notes/.Google Scholar