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On the capacity of uniform hypergraphs
IEEE Transactions on Information Theory, 1990The capacity of uniform hypergraphs can be defined as a natural generalization of the Shannon capacity of graphs. Corresponding to every uniform hypergraph there is a discrete memoryless channel in which the zero error capacity, in the case of the smallest list size for which it is positive, equals the capacity of the hypergraph, and vice versa.
KORNER, JANOS, Katalin Marton
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Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
Symposium on Theoretical Aspects of Computer Science, 2023A linearly ordered (LO) $k$-colouring of a hypergraph is a colouring of its vertices with colours $1, \dots, k$ such that each edge contains a unique maximal colour.
Marek Filakovský +4 more
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Realizing an m-Uniform Four-Chromatic Hypergraph with Disks
Combinatorica, 2020We prove that for every positive integer m there is a finite point set P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Gábor Damásdi, Dömötör Pálvölgyi
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The Uniformity Lemma for hypergraphs
Graphs and Combinatorics, 1992In 1973, E. Szemeredi proved a theorem which found numerous applications in extremal combinatorial problems--The Uniformity Lemma for Graphs. Here we consider an extension of Szemeredi's theorem tor-uniform hypergraphs.
V. Rödl, Peter Frankl
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Regularity method and large deviation principles for the Erdős–Rényi hypergraph
Duke mathematical journal, 2021We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper and lower tails
Nicholas A. Cook, A. Dembo, H. Pham
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Transversals in Linear Uniform Hypergraphs
2020This book gives the state-of-the-art on transversals in linear uniform hypergraphs. The notion of transversal is fundamental to hypergraph theory and has been studied extensively. Very few articles have discussed bounds on the transversal number for linear hypergraphs, even though these bounds are integral components in many applications.
Henning, Michael A, Yeo, Anders
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Exact solution of the hypergraph Turán problem for k-uniform linear paths
Comb., 2011A k-uniform linear path of length ℓ, denoted by ℙℓ(k), is a family of k-sets {F1,...,Fℓ such that |Fi ∩ Fi+1|=1 for each i and Fi ∩ Fbj = $\not 0$ whenever |i−j|>1.
Z. Füredi, T. Jiang, R. Seiver
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On the strong chromatic number of a random 3-uniform hypergraph
Discrete Mathematics, 2021A. E. Balobanov, D. Shabanov
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On the Number of Edges of a Uniform Hypergraph with a Range of Allowed Intersections
Problems of Information Transmission, 2017A. Bobu +4 more
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