Displaying similar documents to “Landau's and Rado's theorems and partial tournaments.”

Maximum Hypergraphs without Regular Subgraphs

Jaehoon Kim, Alexandr V. Kostochka (2014)

Discussiones Mathematicae Graph Theory

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We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1+r−2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.

The Hausdorff dimension of some special plane sets

Jan Mařík (1994)

Mathematica Bohemica

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A compact set T ⊂ 𝐑 2 is constructed such that each horizontal or vertical line intersects T in at most one point while the α -dimensional measure of T is infinite for every α ∈ ( 0 , 2 ) .