descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2018Embargo end date: 01 Jan 2016 English Publisher:Elsevier BVJournal:Discrete Applied Mathematics, volume 237, pages 43-56 (issn: 0166-218X,

Authors: Ryan Bergen; Boting Yang; Karen Meagher; Ferdinand Ihringer; Ferdinand Ihringer; Alison Purdy; Guanglong Yu; +2 Authors

doi: 10.1016/j.dam.2017.11.012 , 10.48550/arxiv.1607.08641

arXiv: http://arxiv.org/abs/1607.08641

handle: 1854/LU-8591060

Infection in hypergraphs

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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.

23 pages

Related Organizations

Ghent University
Belgium
University of Regina
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Yancheng Teachers University
China (People's Republic of)
Hebrew University of Jerusalem
Israel

Keywords

Hypergraphs, ZERO FORCING SETS, GRAPHS, MINIMUM RANK, Mathematics and Statistics, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Zero-forcing, 05C65

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