Saving Colors and Max Coloring: Some Fixed-Parameter Tractability Results

Max coloring is a well known generalization of the usual Min Coloring problem, widely studied from (standard) complexity and approximation viewpoints. Here, we tackle this problem under the framework of parameterized complexity. In particular, we first show to what extend the result of [3] - saving colors from the trivial bound of n on the chromatic number - extends to Max Coloring. Then we consider possible improvements of these results by considering the problem of saving colors/weight with respect to a better bound on the chromatic number. Finally, we consider the fixed parameterized tractability of Max Coloring in restricted graph classes under standard parameterization.