Hedgehog (hypergraph)

In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter t. It has t+(t2) vertices, t of which can be labeled by the integers from 1 to t and the remaining (t2) of which can be labeled by unordered pairs of these integers. For each pair of integers i,j in this range, it has a hyperedge whose vertices have the labels i, j, and {i,j}. Equivalently it can be formed from a complete graph by adding a new vertex to each edge of the complete graph, extending it to an order-3 hyperedge.[1][2]

The properties of this hypergraph make it of interest in Ramsey theory.[1][2]

## References

1. ↑ 1.0 1.1 Conlon, David; Fox, Jacob; Rödl, Vojtěch (2017), "Hedgehogs are not colour blind", Journal of Combinatorics 8 (3): 475–485, doi:10.4310/JOC.2017.v8.n3.a4
2. ↑ 2.0 2.1 Fox, Jacob; Li, Ray (2020), "On Ramsey numbers of hedgehogs", Combinatorics, Probability and Computing 29 (1): 101–112, doi:10.1017/s0963548319000312

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