Infection in Hypergraphs

28 Jul 2016  ·  Bergen Ryan, Fallat Shaun, Gorr Adam, Ihringer Ferdinand, Meagher Karen, Purdy Alison, Yang Boting, Yu Guanglong ·

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. read more

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Combinatorics