Split hypergraphs

TL;DR

This paper extends the concept of split graphs to uniform hypergraphs, providing a finite characterization by excluded subhypergraphs, an algorithm for recognition, and showing the impossibility of degree sequence characterization.

Contribution

It introduces the class of split hypergraphs, characterizes them via forbidden subhypergraphs, and presents an efficient recognition algorithm.

Findings

Characterization by finite forbidden subhypergraphs

Recognition algorithm with $O(N ext{log} N)$ complexity

Impossibility of degree sequence characterization

Abstract

Generalizing the notion of split graphs to uniform hypergraphs, we prove that the class of these hypergraphs can be characterized by a finite list of excluded induced subhypergraphs. We show that a characterization by generalized degree sequences is impossible, unlike in the well-known case of split graphs. We also give an algorithm to decide whether a given uniform hypergraph is a split hypergraph. If it is, the algorithm gives a splitting of it; the running time is $O(N\log N)$. These answer questions of Sloan, Gy. Tur\'an and Peled.