Locally checkable problems parameterized by clique-width
Abstract
We continue the study initiated by Bonomo-Braberman and Gonzalez in 2020 on -locally checkable problems. We propose a dynamic programming algorithm that takes as input a graph with an associated clique-width expression and solves a -locally checkable problem under certain restrictions. We show that it runs in polynomial time in graphs of bounded clique-width, when the number of colors of the locally checkable problem is fixed. Furthermore, we present a first extension of our framework to global properties by taking into account the sizes of the color classes, and consequently enlarge the set of problems solvable in polynomial time with our approach in graphs of bounded clique-width. As examples, we apply this setting to show that, when parameterized by clique-width, the Roman domination problem is FPT, and the -community problem, Max PDS and other variants are XP.
Cite
@article{arxiv.2203.02992,
title = {Locally checkable problems parameterized by clique-width},
author = {Narmina Baghirova and Carolina Lucía Gonzalez and Bernard Ries and David Schindl},
journal= {arXiv preprint arXiv:2203.02992},
year = {2022}
}