At its most basic level, this book is about dominating sets in graphs. A dominating set of a
graph G is a subset D of vertices having the property that each vertex of G is in D or is …

The total domination game is a game played on a graph by 2 players, Dominator and Staller,
who alternate in selecting vertices such that each newly selected vertex increases the …

Abstract The Maker–Breaker domination game is played on a graph G by two players, called
Dominator and Staller, who alternately choose a vertex that has not been played so far …

Let γ g (G) be the game domination number of a graph G. Rall conjectured that if G is a
traceable graph, then γ g (G)≤ 1 2 n (G). Our main result verifies the conjecture over the …

Abstract The 1/2-conjecture on the domination game asserts that if G is a traceable graph,
then the game domination number γg (G) of G is at most A traceable graph is a 1/2-graph if …

The connected domination game on a graph G is played by Dominator and Staller according
to the rules of the standard domination game with the additional requirement that at each …

It is conjectured that the game domination number is at most 3 n∕ 5 for every n-vertex graph
which does not contain isolated vertices. It was proved in the recent years that the conjecture …

The connected domination game was introduced in 2019 by Borowiecki, Fiedorowicz and
Sidorowicz as another variation of the domination game. We answer a problem from their …

The connected domination game is played just as the domination game, with an additional
requirement that at each stage of the game the vertices played induce a connected …

The total domination game is played on a simple graph G with no isolated vertices by two
players, Dominator and Staller, who alternate choosing a vertex in G. Each chosen vertex …