On kernels in strongly game-perfect digraphs and a characterisation of weakly game-perfect digraphs
We prove that the game-perfect digraphs defined by Andres (2012) with regard to a digraph version of the maker-breaker graph colouring game introduced by Bodlaender (1991) always have a kernel. Furthermore, we introduce weakly game-perfect digraphs related to another digraph version of Bodlaender’s...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.03.020 |
| Summary: | We prove that the game-perfect digraphs defined by Andres (2012) with regard to a digraph version of the maker-breaker graph colouring game introduced by Bodlaender (1991) always have a kernel. Furthermore, we introduce weakly game-perfect digraphs related to another digraph version of Bodlaender’s graph colouring game, which was defined by Yang and Zhu (2010), and characterise the classes of weakly game-perfect digraphs by means of the classes of undirected game-perfect graphs. |
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| ISSN: | 0972-8600 2543-3474 |