منابع مشابه
Proper colouring Painter-Builder game
We consider the following two-player game, parametrised by positive integers n and k. The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on n vertices. In each round Painter colours a vertex of her choice by one of the k colours and Builder adds an edge between two previously unconnected vertices. Both player...
متن کاملGame Colouring Directed Graphs
In this paper, a colouring game and two versions of marking games (the weak and the strong) on digraphs are studied. We introduce the weak game chromatic number χwg(D) and the weak game colouring number wgcol(D) of digraphs D. It is proved that if D is an oriented planar graph, then χwg(D) 6 wgcol(D) 6 9, and if D is an oriented outerplanar graph, then χwg(D) 6 wgcol(D) 6 4. Then we study the s...
متن کاملGame List Colouring of Graphs
We consider the two-player game defined as follows. Let (G,L) be a graph G with a list assignment L on its vertices. The two players, Alice and Bob, play alternately on G, Alice having the first move. Alice’s goal is to provide an L-colouring of G and Bob’s goal is to prevent her from doing so. A move consists in choosing an uncoloured vertex v and assigning it a colour from the set L(v). Adjac...
متن کاملGeneralised game colouring of graphs
We consider the version of a colouring game introduced by Bodlaender [On the complexity of some colorings games, Internat. J. Found. Comput. Sci. 2 (1991) 133–147]. We combine the concepts: this game and the generalised colouring of graphs as follows. The two players are Alice and Bob and they play alternatively with Alice having the first move. Let be given a graph G and an ordered set of here...
متن کاملColouring game and generalized colouring game on graphs with cut-vertices
For k ≥ 2 we define a class of graphs Hk = {G : every block of G has at most k vertices}. The class Hk contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from Hk.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.11.008