The orthogonal colouring game
| Autor: | Stephan Dominique Andres, Fionn Mc Inerney, Melissa A. Huggan, Richard J. Nowakowski |
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| Přispěvatelé: | FernUniversität in Hagen, Dalhousie University [Halifax], Combinatorics, Optimization and Algorithms for Telecommunications (COATI), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Rok vydání: | 2019 |
| Předmět: |
Computer Science::Computer Science and Game Theory
mutually orthogonal Latin squares General Computer Science games on graphs 010102 general mathematics 0102 computer and information sciences [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Fixed point scoring game 01 natural sciences 2008 MSC 05C57 05C15 05B15 91A46 91A4 Graph Theoretical Computer Science Combinatorics 010201 computation theory & mathematics strictly matched involution Orthogonal Colouring Game [INFO]Computer Science [cs] 0101 mathematics Graph isomorphism orthogonal graph colouring Mathematics |
| Zdroj: | Theoretical Computer Science Theoretical Computer Science, 2019, 795, pp.312-325 Theoretical Computer Science, Elsevier, 2019, 795, pp.312-325 |
| ISSN: | 0304-3975 1879-2294 |
| DOI: | 10.1016/j.tcs.2019.07.014 |
| Popis: | International audience; We introduce the Orthogonal Colouring Game, in which two players alternately colour vertices (from a choice of m ∈ N colours) of a pair of isomorphic graphs while respecting the properness and the orthogonality of the colouring. Each player aims to maximise her score, which is the number of coloured vertices in the copy of the graph she owns. The main result of this paper is that the second player has a strategy to force a draw in this game for any m ∈ N for graphs that admit a strictly matched involution. An involution σ of a graph G is strictly matched if its fixed point set induces a clique and any non-fixed point v ∈ V (G) is connected with its image σ(v) by an edge. We give a structural characterisation of graphs admitting a strictly matched involution and bounds for the number of such graphs. Examples of such graphs are the graphs associated with Latin squares and sudoku squares. |
| Databáze: | OpenAIRE |
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