Saturation of Berge Hypergraphs
Combinatorics
2017-10-11 v1
Abstract
Given a graph , a hypergraph is a Berge- if it can be obtained by expanding each edge in to a hyperedge containing it. A hypergraph is Berge--saturated if does not contain a subgraph that is a Berge-, but for any edge , does. The -uniform saturation number of Berge- is the minimum number of edges in a -uniform Berge--saturated hypergraph on vertices. For this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in -uniform hypergraphs.
Keywords
Cite
@article{arxiv.1710.03735,
title = {Saturation of Berge Hypergraphs},
author = {Sean English and Nathan Graber and Pamela Kirkpatrick and Abhishek Methuku and Eric C. Sullivan},
journal= {arXiv preprint arXiv:1710.03735},
year = {2017}
}