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Fete of Combinatorics and Computer ScienceColoring Uniform Hypergraphs with Small Edge Degrees

Fete of Combinatorics and Computer Science: Coloring Uniform Hypergraphs with Small Edge Degrees [Let k be a positive integer and n=⌊log2k⌋. We prove that there is an ε = ε(k) > 0 such that for sufficiently large r, every r-uniform hypergraph with maximum edge degree at most \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varepsilon (k)k^r \left( {\frac{r} {{\ln r}}} \right)^{\tfrac{n} {{n + 1}}} $$\end{document} is k-colorable.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fete of Combinatorics and Computer ScienceColoring Uniform Hypergraphs with Small Edge Degrees

Part of the Bolyai Society Mathematical Studies Book Series (volume 20)
Editors: Katona, Gyula O. H.; Schrijver, Alexander; Szőnyi, Tamás; Sági, Gábor
Kostochka, Alexandr V.; Rödl, Vojtěch; Kumbhat, Mohit
Fete of Combinatorics and Computer Science — Jan 31, 2011
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Publisher
Springer Berlin Heidelberg
Copyright
© János Bolyai Mathematical Society and Springer-Verlag 2010
ISBN
978-3-642-13579-8
Pages
213 –238
DOI
10.1007/978-3-642-13580-4_9
Publisher site
See Chapter on Publisher Site

Abstract

[Let k be a positive integer and n=⌊log2k⌋. We prove that there is an ε = ε(k) > 0 such that for sufficiently large r, every r-uniform hypergraph with maximum edge degree at most \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varepsilon (k)k^r \left( {\frac{r} {{\ln r}}} \right)^{\tfrac{n} {{n + 1}}} $$\end{document} is k-colorable.]

Published: Jan 31, 2011

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