Core Concepts
Study and recognize dually conformal hypergraphs efficiently.
Abstract
The content delves into the study of dually conformal hypergraphs, focusing on their properties and recognition algorithms. It covers the basics of hypergraph theory, including Sperner and conformal hypergraphs. The paper explores the relationship between dual conformality and maximal cliques in graphs, providing insights into algorithmic graph theory. Key results include polynomial-time algorithms for recognizing specific cases of dually conformal hypergraphs.
Stats
Given a hypergraph H, its dual hypergraph is always Sperner.
The problem of recognizing dually conformal hypergraphs is in co-NP.
The co-occurrence graph of the dual hypergraph can be computed in O(k|E|∆2|V |2).
The Restricted Dual Conformality problem is solvable in O(k|E|∆2|V |2).
The k-Upper Clique Transversal problem can be solved in O(|V |3k−3).
Quotes
"Hypergraph duality has many applications."
"Every maximal clique in G(Hd) is a transversal of H."
"Recognizing graphs with minimal clique transversals efficiently."