Can I read Connector-Breaker games on random boards on EtoBox?

Connector-Breaker games on random boards by Clemens, Dennis; Kirsch, Laurin; Mogge, Yannick is a scholarly article available to read on EtoBox.

What is Connector-Breaker games on random boards about?

By now, the Maker-Breaker connectivity game on a complete graph $K_n$ or on a random graph $G\sim G_{n,p}$ is well studied. Recently, London and Pluh\'ar suggested a variant in which Maker always needs to choose her edges in such a way that her graph stays connected. By their results it follows that for this connected version of the game, the threshold bias on $K_n$ and the threshold probability on $G\sim G_{n,p}$ for winning the game drastically differ from the corresponding values for the usual Maker-Breaker version, assuming Maker's bias to be $1$. However, they observed that the threshold biases of both versions played on $K_n$ are still of the same order if instead Maker is allowed to claim two edges in every round. Naturally, this made London and Pluh\'ar ask whether a similar phenomenon can be observed when a $(2:2)$ game is played on $G_{n,p}$. We prove that this is not the case, and determine the threshold probability for winning this game to be of size $n^{-2/3+o(1)}$.

Author

Clemens, Dennis; Kirsch, Laurin; Mogge, Yannick

Published

2019

Language

EN