Discrete Mathematics
Ramsey Games Against a One-Armed Bandit
Combinatorics, Probability and Computing
A Large Deviation Result on the Number of Small Subgraphs of a Random Graph
Combinatorics, Probability and Computing
Positional games on random graphs
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
The online clique avoidance game on random graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Small subgraphs in random graphs and the power of multiple choices
Journal of Combinatorial Theory Series B
On balanced coloring games in random graphs
European Journal of Combinatorics
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We introduce and study online balanced coloring games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are introduced two at a time, in a random order. For each pair of edges, Painter immediately and irrevocably chooses one of the two possibilities to color one of them red and the other one blue. His goal is to avoid creating a monochromatic copy of a small fixed graph F for as long as possible. We show that the duration of the game is determined by a threshold function m"H=m"H(n) for certain graph-theoretic structures, e.g., cycles. That is, for every graph H in this family, Painter will asymptotically almost surely (a.a.s.) lose the game after m=@w(m"H) edge pairs in the process. On the other hand, there exists an essentially optimal strategy: if the game lasts for m=o(m"H) moves, Painter can a.a.s. successfully avoid monochromatic copies of H. Our attempt is to determine the threshold function for several classes of graphs.