Harmonious Coloring: Parameterized Algorithms and Upper Bounds

Sudeshna Kolay, Ragukumar Pandurangan, Fahad Panolan, Venkatesh Raman, Prafullkumar Tale

Abstract: A harmonious coloring of a graph is a partitioning of its vertex set into parts such that, there are no edges inside each part, and there is at most one edge between any pair of parts. It is known that finding a minimum harmonious coloring number is NP-hard even in special classes of graphs like trees and split graphs.