Picker-Chooser fixed graph games

Abstract

Given a fixed graph $H$ and a positive integer $n$, a Picker-Chooser $H$-game is a biased game played on the edge set of $K_n$ in which Picker is trying to force many copies of $H$ and Chooser is trying to prevent him from doing so. In this paper we conjecture that the value of the game is roughly the same as the expected number of copies of $H$ in the random graph $G(n,p)$ and prove our conjecture for special cases of $H$ such as complete graphs and trees.

References in corpus (1)

• Two constructions relating to conjectures of Beck on positional games

Cited by in corpus (1)

• Waiter-Client and Client-Waiter planarity, colorability and minor games