A vertex subset D of a graph G is a dominating set if every vertex of G is either in D or is adjacent to a vertex in D. The paired-domination problem on G asks for a minimum-cardinality dominating set S of G such that the subgraph induced by S contains a perfect matching; motivation for this problem comes from the interest in finding a small number of locations to place pairs of mutually visibl...

Abstra t A vertex subset D of a graph G is a dominating set if every vertex of G is either in D or is adja ent to a vertex in D. The paired domination problem on G asks for a minimumardinality dominating set S of G su h that the subgraph indu ed by S ontains a perfe t mat hing; motivation for this problem omes from the interest in nding a small number of lo ations to pla e pairs of mutually vis...

This paper examines the relationship between coalition-proof Nash equilibria based on different dominance relations. Konishi, Le Breton, and Weber (1999) pointed out that the set of coalition-proof Nash equilibria under weak domination does not necessarily coincide with that under strict domination. We show that, if a game satisfies the conditions of anonymity, monotone externality, and strateg...

A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69– 75] established the followin...

The 34 -Game Total Domination Conjecture posed by Henning, Klavžar and Rall [Combinatorica, to appear] states that if G is a graph on n vertices in which every component contains at least three vertices, then γtg(G) ≤ 34n, where γtg(G) denotes the game total domination number of G. Motivated by this conjecture, we raise the problem to a higher level by introducing a transversal game in hypergra...

Two players, Dominator and Staller, alternate choosing vertices of a graph G, one at a time, such that each chosen vertex enlarges the set of vertices dominated so far. The aim of the Dominator is to finish the game as soon as possible, while the aim of the Staller is just the opposite. The game domination number γg(G) is the number of vertices chosen when Dominator starts the game and both pla...