Contains a wealth of information previously scattered in research journals, conference
proceedings and technical reports. Identifies more than 200 unsolved problems. Every …

In this paper we consider the following game: players must alternately color the lowest
numbered uncolored vertex of a given graph G=({1, 2,…, n}, E) with a color, taken from a …

We survey the literature on those variants of the {\em chromatic number\/} problem where not
only a proper coloring has to be found (ie, adjacent vertices must not receive the same color) …

We show that the game chromatic number of a planar graph is at most 33. More generally,
there exists a function f: ℕ→ ℕ so that for each n∈ ℕ, if a graph does not contain a …

This paper discusses a variation of the game chromatic number of a graph: the game
coloring number. This parameter provides an upper bound for the game chromatic number …

Game chromatic number of outerplanar graphs Page 1 Game Chromatic Number of
Outerplanar Graphs DJ Guan and Xuding Zhu DEPARTMENT OF APPLIED MATHEMATICS …

Many graph theoretic algorithms rely on an initial ordering of the vertices of the graph which
has some special properties. We discuss new ways to measure the quality of such orders …

We show that if a graph has acyclic chromatic number k, then its game chromatic number is
at most k (k+ 1). By applying the known upper bounds for the acyclic chromatic numbers of …

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 …

We prove that the game coloring number, and therefore the game chromatic number, of a
planar graph is at most 18. This is a slight improvement of the current upper bound of 19 …