Upper Bounds for Positional Paris-Harrington Games

  title={Upper Bounds for Positional Paris-Harrington Games},
  author={Lorenzo Carlucci and Massimo Lauria},
We give upper bounds for a positional game — in the sense of Beck — based on the Paris-Harrington principle for bi-colorings of graphs and uniform hypergraphs of arbitrary dimension. The bounds show a striking difference with respect to the bounds of the combinatorial principle itself. Our results confirm a phenomenon already observed by Beck and others: the upper bounds for the game version of a combinatorial principle are drastically smaller than the upper bounds for the principle itself. In… CONTINUE READING