On the complexity of some coloring games
WG '90 Proceedings of the 16th international workshop on Graph-theoretic concepts in computer science
Graphs with linearly bounded Ramsey numbers
Journal of Combinatorial Theory Series B
Planar graph coloring with an uncooperative partner
Journal of Graph Theory
Journal of Graph Theory
A bound for the game chromatic number of graphs
Discrete Mathematics
The game coloring number of planar graphs
Journal of Combinatorial Theory Series B
The game coloring number of pseudo partial k-trees
Discrete Mathematics
A simple competitive graph coloring algorithm
Journal of Combinatorial Theory Series B
Relaxed game chromatic number of graphs
Discrete Mathematics
List Improper Colourings of Planar Graphs
Combinatorics, Probability and Computing
Game chromatic number of outerplanar graphs
Journal of Graph Theory
Game chromatic index of k-degenerate graphs
Journal of Graph Theory
A simple competitive graph coloring algorithm III
Journal of Combinatorial Theory Series B
Hi-index | 0.00 |
We consider the following game played on a finite graph G. Let r and d be positive integers. Two players, Alice and Bob, alternately color the vertices of G, using colors from a set of colors X, with |X| = r. A color α ∈ X is a legal color for uncolored vertex v if by coloring v with color α, the subgraph induced by all vertices of color α has maximum degree at most d. Each player is required to color legally on each turn. Alice wins the game if all vertices of the graph are legally colored. Bob wins if there comes a time when there exists an uncolored vertex which cannot be legally colored. We show that if G is a partial k-tree, r = k + 1, and d ≥ 4k - 1, then Alice has a winning strategy for this game. In the special case that k = 1, this answers a question of Chou, Wang, and Zhu. We also analyze this strategy for other classes of graphs. In particular, we show that there exists a positive integer d such that Alice can win the game on any planar graph if r = 6.