The domination game played on a graph G consists of two players, Dominator and Staller,
who alternate taking turns choosing a vertex from G such that whenever a vertex is chosen …

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 …

Roughly speaking, the family of combinatorial games consists of two-player games with
perfect information (no hidden information as in some card games), no chance moves (no …

This article proves the following result: Let G and G′ be graphs of orders n and n′,
respectively. Let G* be obtained from G by adding to each vertex a set of n′ degree 1 …

In 2020, Costa et al. answered a long-standing open question, proposed by Bodlaender in
1991: the graph coloring game is PSPACE-complete. They also proved that the greedy …

The graph coloring game is a two-player game in which the two players properly color an
uncolored vertex of G alternately. The first player wins the game if all vertices of G are …

In this paper, we answer a long-standing open question proposed by Bodlaender in 1991:
the game chromatic number is PSPACE-hard. We also prove that the game Grundy number …

The thinness of a graph is a width parameter that generalizes some properties of interval
graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be …

The Game Chromatic Number of Some Families of Cartesian Product Graphs Page 1 AKCE J.
Graphs. Combin., 6, No. 2 (2009), pp. 315-327 The Game Chromatic Number of Some Families …

Very recently, a long-standing open question proposed by Bodlaender in 1991 was
answered: the graph coloring game is PSPACE-complete. In 2019, Andres and Lock …