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 weights.

Rights

URN

URN:NBN:SI:doc-B9DVANX6

COBISSID

202315011

DOI

10.26493/1855-3974.2771.4df

Added

13.11.2024

Metadata

Citation

APA:

Bujtás, Csilla, Rote, Günter, Tuza, Zsolt (2024). Optimal strategies in fractional games: vertex cover and domination. Ars mathematica contemporanea, volume 24, issue 3, article p3.05, 19 str. URN:NBN:SI:doc-B9DVANX6 from http://www.dlib.si

MLA:

Bujtás, Csilla, Rote, Günter, Tuza, Zsolt. "Optimal strategies in fractional games: vertex cover and domination." Ars mathematica contemporanea volume 24. issue 3. article p3.05 (2024) 19 str..
<http://www.dlib.si/?URN=URN:NBN:SI:doc-B9DVANX6>

Ars mathematica contemporanea
2008-
(Assembly record)