منابع مشابه
Game 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 کاملAdapted list colouring of planar graphs
Given a (possibly improper) edge-colouring F of a graph G, a vertex colouring of G is adapted to F if no colour appears at the same time on an edge and on its two endpoints. If for some integer k, a graph G is such that given any list assignment L to the vertices of G, with |L(v)| ≥ k for all v, and any edgecolouring F of G, G admits a colouring c adapted to F where c(v) ∈ L(v) for all v, then ...
متن کاملGame colouring of the square of graphs
This paper studies the game chromatic number and game colouring number of the square of graphs. In particular, we prove that if G is a forest of maximum degree ∆ ≥ 9, then χg(G ) ≤ colg(G ) ≤ ∆+3, and there are forestsG with colg(G ) = ∆+3. It is also proved that for an outerplanar graph G of maximum degree ∆, χg(G ) ≤ colg(G ) ≤ 2∆ + 14, and for a planar graph G of maximum degree ∆, χg(G ) ≤ c...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.11.001