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arXiv · 1607.08641

Infection in Hypergraphs

Ryan Bergen·Shaun Fallat·Adam Gorr·Ferdinand Ihringer·Karen Meagher·Alison Purdy·Boting Yang·Guanglong Yu
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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.

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Ryan Bergen, Shaun Fallat, Adam Gorr, Ferdinand Ihringer, Karen Meagher, Alison Purdy, Boting Yang, Guanglong Yu. 2016-07-28. Infection in Hypergraphs. https://arxiv.org/abs/1607.08641

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