TL;DR
This paper investigates F-saturation games on complete graphs, providing bounds and precise results for games avoiding paths, trees, and stars, thereby advancing understanding of game lengths in graph theory.
Contribution
It offers new lower bounds and exact results for the length of F-saturation games avoiding specific graph classes, extending prior work on these combinatorial games.
Findings
Lower bounds on path-avoiding games
Precise results for short paths
Sharp results for tree and star avoiding games
Abstract
We study F-saturation games, first introduced by F\"uredi, Reimer and Seress in 1991, and named as such by West. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We show lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding 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
TopicsGame Theory and Applications · Economic theories and models · Game Theory and Voting Systems