Fast winning strategies in Avoider-Enforcer games
Dan Hefetz, Michael Krivelevich, Milo\v{s} Stojakovi\'c, Tibor Szab\'o

TL;DR
This paper investigates the minimum number of moves required for Enforcer to win certain Avoider-Enforcer games on complete graphs, providing precise estimates for games like non-planarity, connectivity, and non-bipartiteness.
Contribution
It introduces the study of game duration in Avoider-Enforcer games and offers precise bounds for Enforcer's winning time in several known winning scenarios.
Findings
Estimated minimum moves for Enforcer to win in various games
Precise bounds for non-planarity, connectivity, and non-bipartiteness games
Initiation of duration analysis in Avoider-Enforcer games
Abstract
In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not {\em who} wins but rather {\em how fast} can one win. These type of problems were studied earlier for Maker-Breaker games; here we initiate their study for unbiased Avoider-Enforcer games played on the edge set of the complete graph on vertices. For several games that are known to be an Enforcer's win, we estimate quite precisely the minimum number of moves Enforcer has to play in order to win. We consider the non-planarity game, the connectivity game and the non-bipartite game.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Artificial Intelligence in Games · Game Theory and Applications
