Parameterized Coloring Problems on Threshold Graphs
I.Vinod Reddy
TL;DR
This paper investigates the parameterized complexity of various graph coloring problems on special graph classes, establishing fixed-parameter tractability results and computational hardness in different scenarios.
Contribution
It demonstrates that certain coloring problems are FPT on threshold and split graphs, providing new algorithmic insights and complexity classifications.
Findings
Precoloring Extension is FPT by distance to clique
Equitable Coloring is FPT by distance to threshold graphs
List k-Coloring is NP-complete on split graphs and FPT by solution size
Abstract
In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is FPT parameterized by the distance to threshold graphs. We also study the List k-Coloring and show that the problem is NP-complete on split graphs and it is FPT parameterized by solution size on split graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Nuclear Receptors and Signaling