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 …

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 …

Refined activation strategy for the marking game Page 1 Journal of Combinatorial Theory,
Series B 98 (2008) 1–18 www.elsevier.com/locate/jctb Refined activation strategy for the …

An oriented graph is a loopless digraph with no opposite arcs. An oriented k-colouring of an
oriented graph G ⃗ is a partition of its set of vertices into k parts in such a way that no two …

1. INTRODUCTION. Suppose that Alice wants to color a planar map using four colors in a
proper way, that is, so that any two adjacent regions get different colors. Despite the fact that …

The game chromatic number $\chi _ {g} $ is considered for the Cartesian product $
G\,\square\, H $ of two graphs $ G $ and $ H $. Exact values of $\chi _ {g}(K_2\square H) …

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 …

Given a graph G and an integer k, two players take turns coloring the vertices of G one by
one using k colors so that neighboring vertices get different colors. The first player wins iff at …

Nešetřil and Sopena introduced a concept of oriented game chromatic number and
developed a general technique for bounding this parameter. In this paper, we combine their …

The game chromatic number and the game colouring number of cactuses Page 1 Information
Processing Letters 102 (2007) 147–151 www.elsevier.com/locate/ipl The game chromatic …