Английская Википедия:Hedgehog (hypergraph)

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Шаблон:Distinguish In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter <math>t</math>. It has <math>t+\tbinom{t}{2}</math> vertices, <math>t</math> of which can be labeled by the integers from <math>1</math> to <math>t</math> and the remaining <math>\tbinom{t}{2}</math> of which can be labeled by unordered pairs of these integers. For each pair of integers <math>i,j</math> in this range, it has a hyperedge whose vertices have the labels <math>i</math>, <math>j</math>, and <math>\{i,j\}</math>. 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.Шаблон:R

The properties of this hypergraph make it of interest in Ramsey theory.Шаблон:R