The Complexity of 2-Intersection Graphs of 3-Hypergraphs Recognition for Claw-free Graphs and triangulated Claw-free Graphs
Combinatorics
2023-05-24 v1
Abstract
Given a 3-uniform hypergraph H, its 2-intersection graph G has for vertex set the hyperedges of H and ee' is an edge of G whenever e and e' have exactly two common vertices in H. Di Marco et al. prove that deciding wether a graph G is the 2-intersection graph of a 3-uniform hypergraph is NP-complete. The main problems we study concern the class of claw-free graphs. We show that the recognition problem remains NP-complete when G is claw-free graphs but becomes polynomial if in addition G is triangulated.
Keywords
Cite
@article{arxiv.2305.13932,
title = {The Complexity of 2-Intersection Graphs of 3-Hypergraphs Recognition for Claw-free Graphs and triangulated Claw-free Graphs},
author = {Niccolò Di Marco and Andrea Frosini and Christophe Picouleau},
journal= {arXiv preprint arXiv:2305.13932},
year = {2023}
}