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arXiv · 2105.03890

Optimal strategies in fractional games: vertex cover and domination

Csilla Bujtás·Günter Rote·Zsolt Tuza
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Abstract

In a hypergraph with vertex set $V$ and edge set $E$, a real-valued function $f: V \to [0, 1]$ is a fractional transversal if $\sum_{v\in e} f(v) \ge 1$ for every edge $e \in E$. Its size is $|f| := \sum_{v \in V} f(v)$, and the fractional transversal number is the smallest possible $|f|$. We consider a game scenario where two players with opposite goals construct a fractional transversal incrementally, trying to minimize and maximize $|f|$, respectively. We prove that both players have strategies to achieve their common optimum, and they can reach their goals using rational weights.

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Csilla Bujtás, Günter Rote, Zsolt Tuza. 2021-05-09. Optimal strategies in fractional games: vertex cover and domination. https://arxiv.org/abs/2105.03890

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