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Inequalities relating degrees of adjacent vertices to the average degree. (English) Zbl 0624.05048

By a hypergraph with a fixed number of vertices (per edge), say n, the authors understand a matrix of non-negative integers with constant row sum n; they allow vertices to occur more than once in an edge. The authors prove a theorem from which they draw four corollaries. One of them states that the geometric degree of the vertices is not less than the arithmetic degree. Another corollary relates the number of edge, the number of vertices, and the largest number of triangles based on a fixed edge.
Reviewer: L.Zaremba

MSC:

05C65 Hypergraphs

Keywords:

n-hypergraph
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References:

[1] Bollobás, B., Extremal graph theory, (1978), Academic Press London · Zbl 0419.05031
[2] Hardy, Littlewood and polya, (1934), Inequalities Cambridge University Press
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