Ramsey properties of random graphs
Journal of Combinatorial Theory Series B
Ramsey Games Against a One-Armed Bandit
Combinatorics, Probability and Computing
Online vertex colorings of random graphs without monochromatic subgraphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Online ramsey games in random graphs
Combinatorics, Probability and Computing
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
Online ramsey games in random graphs
Combinatorics, Probability and Computing
Coloring random graphs online without creating monochromatic subgraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Consider the following one-player game. Starting with the empty graph on n vertices, in every step a new edge is drawn uniformly at random and inserted into the current graph. This edge has to be coloured immediately with one of r available colours. The player's goal is to avoid creating a monochromatic copy of some fixed graph F for as long as possible. We prove an upper bound on the typical duration of this game if F is from a large class of graphs including cliques and cycles of arbitrary size. Together with lower bounds published elsewhere, explicit threshold functions follow.