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Minimal 2-dominating sets in trees

Marcin Krzywkowski — 2013

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We provide an algorithm for listing all minimal 2-dominating sets of a tree of order in time 𝒪(1.3248). This implies that every tree has at most 1.3248 minimal 2-dominating sets. We also show that this bound is tight.

A modified hat problem

Marcin Krzywkowski — 2010

Commentationes Mathematicae

The topic of our paper is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultane- ously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. There are known many variations of the hat problem. In this paper we consi- der a variation...

The hat problem on a union of disjoint graphs

Marcin Krzywkowski — 2011

Commentationes Mathematicae

The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. In this version every player can see everybody excluding himself. We consider such a problem on a...

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