English

Infection in Hypergraphs

Combinatorics 2016-08-01 v1

Abstract

In this paper a new parameter for hypergraphs called hypergraph infection is defined. This concept generalizes zero forcing in graphs to hypergraphs. The exact value of the infection number of complete and complete bipartite hypergraphs is determined. A formula for the infection number for interval hypergraphs and several families of cyclic hypergraphs is given. The value of the infection number for a hypergraph whose edges form a symmetric t-design is given, and bounds are determined for a hypergraph whose edges are a t-design. Finally, the infection number for several hypergraph products and line graphs are considered.

Keywords

Cite

@article{arxiv.1607.08641,
  title  = {Infection in Hypergraphs},
  author = {Ryan Bergen and Shaun Fallat and Adam Gorr and Ferdinand Ihringer and Karen Meagher and Alison Purdy and Boting Yang and Guanglong Yu},
  journal= {arXiv preprint arXiv:1607.08641},
  year   = {2016}
}

Comments

23 pages

R2 v1 2026-06-22T15:07:16.190Z