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arXiv · 2305.13932

The Complexity of 2-Intersection Graphs of 3-Hypergraphs Recognition for Claw-free Graphs and triangulated Claw-free Graphs

Niccolò Di Marco·Andrea Frosini·Christophe Picouleau
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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.

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Niccolò Di Marco, Andrea Frosini, Christophe Picouleau. 2023-05-23. The Complexity of 2-Intersection Graphs of 3-Hypergraphs Recognition for Claw-free Graphs and triangulated Claw-free Graphs. https://arxiv.org/abs/2305.13932

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