Independent sets in edge-clique graphs II
Ching-Hao Liu, Ton Kloks, Sheung-Hung Poon
TL;DR
This paper investigates the computational complexity of the independent set problem in edge-clique graphs across various graph classes, providing complexity results, conjectures, and approximation algorithms.
Contribution
It establishes NP-completeness results for certain graph classes, proposes a PTAS for planar graphs, and conjectures NP-completeness of the edge-clique cover problem for cographs.
Findings
Edge-clique graphs of cocktail party graphs have unbounded rankwidth.
NP-completeness of the independent set problem on edge-clique graphs of cographs.
A PTAS for the independent set problem on planar graphs.
Abstract
We show that edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem on edge-clique graphs of cographs. We show that the independent set problem on edge-clique graphs of graphs without odd wheels remains NP-complete. We present a PTAS for planar graphs and show that the problem is polynomial for planar graphs without triangle separators.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory