Strong Ramsey game on two boards
Jiangdong Ai, Jun Gao, Zixiang Xu, Xin Yan

TL;DR
This paper investigates a variant of the strong Ramsey game played on two disjoint complete graphs, proving the existence of infinitely many target graphs for which the first player cannot win in a bounded number of moves, shedding light on a longstanding open problem.
Contribution
It introduces and analyzes the game on two disjoint boards, demonstrating infinitely many graphs where the first player lacks a bounded winning strategy, advancing understanding of the open problem.
Findings
Existence of infinitely many graphs $H$ with no bounded winning strategy for $P_1$ on $K_n K_n$
Concise proof establishing non-existence of bounded winning strategies in the variant game
Evidence supporting the possibility of graphs that challenge the longstanding open problem
Abstract
The strong Ramsey game is a two-player game played on a graph , referred to as the board, with a target graph . In this game, two players, and , alternately claim unclaimed edges of , starting with . The goal is to claim a subgraph isomorphic to , with the first player achieving this declared the winner. A fundamental open question, persisting for over three decades, asks whether there exists a graph such that in the game , does not have a winning strategy in a bounded number of moves as . In this paper, we shift the focus to the variant , introduced by David, Hartarsky, and Tiba, where the board consists of two disjoint copies of . We prove that there exist infinitely many graphs such that cannot win in …
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.
