Random Coloring

Given an undirected graph $G$ with $N$ nodes, where every node is initially uncolored, Chef colors its vertices either red or blue by the following process: - Chef will perform exactly $N$ coloring operations, one for each vertex. - At the time of the $i$-th operation, let $R$ denote the number of red nodes and $B$ denote the number of blue nodes. Chef colors node $i$ red with a probability of $