467 KB55 KB200820252024Bujtás, CsillaRote, GünterTuza, Zsolt19 str.letnik:24številka:3, article p3.05DOI:10.26493/1855-3974.2771.4dfISSN:1855-3966COBISSID_HOST:202315011URN:URN:NBN:SI:doc-B9DVANX6enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneafractional domination gamefractional transversal gamefractional vertex coverOptimal strategies in fractional games: vertex cover and domination|In 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 weightsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije