A Finite Characterization and Recognition of Intersection Graphs of Hypergraphs with Rank at Most 3 and Multiplicity at Most 2 in the Class of Threshold Graphs

Abstract

We characterize the class L32$L_3^2 $ of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from L32$L_3^2 $ in the class of threshold graphs, where n is the number of vertices of a tested graph.

Keywords

• intersection graph
• hypergraph rank
• hypergraph multiplicity
• forbidden induced subgraph
• threshold graph
• 05c62
• 05c75
• 05c70
• 05c65
• 05c85