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On Ramsey-type problems for paths and cycles with few colour changes
Peter Allen, Julia Böttcher, Dennis Clemens +3
In 1967, Gerencser and Gyárfás determined the exact values of the two-colour Ramsey numbers of paths. In a footnote, they made the following observation: Every -edge-coloured co…
Constructions for positional games and applications to domination games
Ali Deniz Bagdas, Dennis Clemens, Fabian Hamann +1
We present constructions regarding the general behaviour of biased positional games, and amongst others show that the outcome of such a game can differ in an arbitrary way dependin…
Maker playing against an invisible Breaker
Dennis Clemens, Fabian Hamann, Mirjana Mikalački +2
We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has t…
Biased domination games
Ali Deniz Bagdas, Dennis Clemens, Fabian Hamann +1
We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{š}i{č}, and Klav{ž}ar. Two players, Dominator and Staller, alternatingl…
Positional games on randomly perturbed graphs
Dennis Clemens, Fabian Hamann, Yannick Mogge +1
Maker-Breaker games are played on a hypergraph , where denotes the family of winning sets. Both players alternately claim a predefined…