Coloring Uniform Hypergraphs with Small Edge Degrees

Kostochka, Alexandr V.; Rödl, Vojtěch; Kumbhat, Mohit

doi:10.1007/978-3-642-13580-4_9

Coloring Uniform Hypergraphs with Small Edge Degrees

Alexandr V. Kostochka⁵,
Vojtěch Rödl⁶ &
Mohit Kumbhat⁷

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 20))

Abstract

Let k be a positive integer and n=⌊log₂ k⌋. 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

$$ \varepsilon (k)k^r \left( {\frac{r} {{\ln r}}} \right)^{\tfrac{n} {{n + 1}}} $$

is k-colorable.

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Authors and Affiliations

University of Illinois, Urbana, IL, 61801 and Institute of Mathematics, Novosibirsk, 630090, Russia
Alexandr V. Kostochka
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
Vojtěch Rödl
Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA
Mohit Kumbhat

Authors

Alexandr V. Kostochka
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Vojtěch Rödl
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Mohit Kumbhat
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Editor information

Editors and Affiliations

Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary
Gyula O. H. Katona
Centre for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands
Alexander Schrijver
Department of Computer Science, Eötvös University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary
Tamás Szőnyi
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary
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Kostochka, A.V., Rödl, V., Kumbhat, M. (2010). Coloring Uniform Hypergraphs with Small Edge Degrees. In: Katona, G.O.H., Schrijver, A., Szőnyi, T., Sági, G. (eds) Fete of Combinatorics and Computer Science. Bolyai Society Mathematical Studies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13580-4_9

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DOI: https://doi.org/10.1007/978-3-642-13580-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13579-8
Online ISBN: 978-3-642-13580-4
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