Parameterized and Exact Algorithms for Class Domination Coloring
R. Krithika, Ashutosh Rai, Saket Saurabh, Prafullkumar Tale

TL;DR
This paper introduces exact and parameterized algorithms for class domination coloring, analyzing computational complexity and providing fixed-parameter tractability results for specific graph classes and parameters.
Contribution
It presents new algorithms and complexity results for the class domination coloring problem, including an exact exponential-time algorithm and fixed-parameter tractability on certain graph classes.
Findings
Exact algorithm with (2^n n^4 \,\log n) time for cd-chromatic number
FPT algorithms for chordal and split graphs under certain parameters
NP-hardness results for vertex deletion problems related to cd-coloring
Abstract
A class domination coloring (also called cd-Coloring or dominated coloring) of a graph is a proper coloring in which every color class is contained in the neighbourhood of some vertex. The minimum number of colors required for any cd-coloring of , denoted by , is called the class domination chromatic number (cd-chromatic number) of . In this work, we consider two problems associated with the cd-coloring of a graph in the context of exact exponential-time algorithms and parameterized complexity. (1) Given a graph on vertices, find its cd-chromatic number. (2) Given a graph and integers and , can we delete at most vertices such that the cd-chromatic number of the resulting graph is at most ? For the first problem, we give an exact algorithm with running time . Also, we show that the problem is \FPT\ with respect to the…
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