Note on Polychromatic Coloring of Hereditary Hypergraph Families

We exhibit a 5-uniform hypergraph that has no polychromatic 3-coloring, but all its restricted subhypergraphs with edges of size at least 3 are 2-colorable. This disproves a bold conjecture of Keszegh and the author, and can be considered as the first step to understand polychromatic colorings of he...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 40; no. 6; p. 131
Main Author Pálvölgyi, Dömötör
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.12.2024
Springer Nature B.V
Subjects
Coloring
Combinatorics
Engineering Design
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
Polychromatic coloring
Hypergraphs
Graph colorings
05C15 (Coloring of graphs and hypergraphs)
Panchromatic coloring
Online AccessGet full text
ISSN0911-0119
1435-5914
1435-5914
DOI10.1007/s00373-024-02836-y

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Summary:We exhibit a 5-uniform hypergraph that has no polychromatic 3-coloring, but all its restricted subhypergraphs with edges of size at least 3 are 2-colorable. This disproves a bold conjecture of Keszegh and the author, and can be considered as the first step to understand polychromatic colorings of hereditary hypergraph families better since the seminal work of Berge. We also show that our method cannot give hypergraphs of arbitrary high uniformity, and mention some connections to panchromatic colorings.
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ISSN:0911-0119
1435-5914
1435-5914
DOI:10.1007/s00373-024-02836-y