On kernels in strongly game-perfect digraphs and a characterisation of weakly game-perfect digraphs
Stephan Dominique Andres · AKCE International Journal of Graphs and Combinatorics · 2019
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.