Optimal strategies in fractional games: vertex cover and dominationBujtás, Csilla (Avtor) Rote, Günter (Avtor) Tuza, Zsolt (Avtor) fractional vertex coverfractional transversal gamefractional domination gameIn a hypergraph ${\cal H}=(V,{\cal E})$ with vertex set $V$ and edge set ${\cal E}$, 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 $E \in {\cal E}$. Its size is $|f| := \sum_{v \in V} f(v)$, and the fractional transversal number $\tau^\ast({\cal H})$ is the smallest possible $|f|$. We consider a game scenario where two players have opposite goals, one of them trying to minimize and the other to maximize the size of a fractional transversal constructed incrementally. We prove that both players have strategies to achieve their common optimum, and they can reach their goals using rational weights.20242025-01-24 13:23:08Članek v reviji166787sl