MathDBBeck's Chooser-Picker conjecture
Beck's Chooser-Picker conjecture
Let be a hypergraph. Suppose that Breaker wins the Maker-Breaker game on , with Maker moving first. Beck's Chooser-Picker conjecture. Picker wins the Chooser-Picker game on . This conjecture compares the relative difficulty of the Maker-Breaker and Chooser-Picker games on the same hypergraph. It is refuted by a construction in this paper: there is a hypergraph on which Breaker wins the Maker-Breaker game while Chooser wins the Chooser-Picker game.
Sources & referencesView supporting material
Primary source
Fiachra Knox, “Two constructions relating to conjectures of Beck on positional games”, arXiv:1212.3345 (2012).
Additional references
2 papers in this index state this conjecture (2010–2012). The statement above is taken from the most recent of them; the others are arXiv:1004.2460.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.