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Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs

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SOFSEM 2012: Theory and Practice of Computer Science (SOFSEM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7147))

Abstract

We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.

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Author information

Authors and Affiliations

  1. Center for Advanced Studies in Mathematics, Ben-Gurion University, Be’er Sheva, Israel

    Panagiotis Cheilaris

  2. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Balázs Keszegh

  3. Eötvös University, Budapest, Hungary

    Dömötör Pálvölgyi

Authors
  1. Panagiotis Cheilaris
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  2. Balázs Keszegh
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  3. Dömötör Pálvölgyi
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Editor information

Editors and Affiliations

  1. Faculty of Informatics and Information Technologies, Institute of Informatics and Software Engineering, Slovak University of Technology in Bratislava, Ilkovičova 3, 842 16, Bratislava 4, Slovakia

    Mária Bieliková

  2. Dept. of Intelligent Systems and Business Informatics, Alpen-Adria-Universität Klagenfurt, Universitätsstr. 65-57, 9020, Klagenfurt, Austria

    Gerhard Friedrich

  3. Department of Computer Science, University of Oxford, UK

    Georg Gottlob

  4. Security Engineering Group, Technische Universität Darmstadt, Hochschulstr. 10, 64289, Darmstadt, Germany

    Stefan Katzenbeisser

  5. University of Illinois at Chicago, Dept. of Math., Stat. and Comp. Sci, 851 S. Morgan Street, Chicago, IL 60607-7045, USA; and University of Szeged, Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, 6701 Szeged, Postafiók, Hungary

    György Turán

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© 2012 Springer-Verlag Berlin Heidelberg

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Cheilaris, P., Keszegh, B., Pálvölgyi, D. (2012). Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_16

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  • DOI: https://doi.org/10.1007/978-3-642-27660-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27659-0

  • Online ISBN: 978-3-642-27660-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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