Parameterized maximum path coloring

We study the well-known Max Path Coloring problem from a parameterized point of view, focusing on trees and low-treewidth networks. We observe the existence of a variety of reasonable parameters for the problem, such as the maximum degree and treewidth of the network graph, the number of available colors and the number of requests one seeks to satisfy or reject. In an effort to understand the impact of each of these parameters on the problem’s complexity we study various parameterized versions of the problem deriving fixed-parameter tractability and hardness results both for undirected and bi-directed graphs.