arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.06735math.CO
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明星回避游戏

The star avoidance game

Adrian Beker

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6 pages
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摘要：

设$n, k$为正整数。$K_n$上的$(k+1)$ -星回避游戏如下进行。两个参与者轮流在$n$顶点上声明完全图的一条（以前未声明的）边。第一个声称子图的所有边同构于$(k+1)$ -星的玩家输。等价地，每个参与者必须保持由其边形成的子图中的所有度至多为$k$。如果所有的边都被选上了，并且没有一个玩家输了，那么游戏就被宣布为平局。我们证明，对于每个固定的$k$，游戏是一个胜利的第二个球员的所有$n$足够大。

英文摘要：

Let $n, k$ be positive integers. The $(k+1)$-star avoidance game on $K_n$ is played as follows. Two players take it in turn to claim a (previously unclaimed) edge of the complete graph on $n$ vertices. The first player to claim all edges of a subgraph isomorphic to a $(k+1)$-star loses. Equivalently, each player must keep all degrees in the subgraph formed by his edges at most $k$. If all edges have been chosen and neither player has lost, the game is declared a draw. We prove that, for each fixed $k$, the game is a win for the second player for all $n$ sufficiently large.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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