On Balanced Coloring Games in Random Graphs

Balanced Online Edge Coloring Games on Random Graphs

Balanced Avoidance Games on Random Graphs

We introduce and study balanced online graph avoidance 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 revealed two at a time in a random order. In each move, Painter immediately and irrevocably decides on a balanced coloring of the new edge pair: either the first edge is colored red and the second one blue or vi...

Balanced Online Ramsey Games in Random Graphs

Consider the following one-player game. Starting with the empty graph on n vertices, in every step r new edges are drawn uniformly at random and inserted into the current graph. These edges have to be colored immediately with r available colors, subject to the restriction that each color is used for exactly one of these edges. The player’s goal is to avoid creating a monochromatic copy of some ...

Online balanced graph avoidance games

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 the 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 crea...

Games on Graphs

We introduce and study Maker-Breaker positional games on random graphs. Our goal is to determine the threshold probability p F for the existence of Maker's strategy to claim a member of F in the unbiased (one-on-one) game played on the edges of the random graph G(n, p), for various target families F of winning sets. More generally, for each probability above this threshold we study the smallest...