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Horizons of Combinatorics pp 235–255Cite as

Problems and Results on Colorings of Mixed Hypergraphs

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 17))

Abstract

We survey results and open problems on ‘mixed hypergraphs’ that are hypergraphs with two types of edges. In a proper vertex coloring the edges of the first type must not be monochromatic, while the edges of the second type must not be completely multicolored. Though the first condition just means ‘classical’ hypergraph coloring, its combination with the second one causes rather unusual behavior. For instance, hypergraphs occur that are uncolorable, or that admit colorings with certain numbers k′ and k″ of colors but no colorings with exactly k colors for any k′ < k < k″.

Research supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613.

Partially supported by Troy University Research Grant.

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Author information

Authors and Affiliations

  1. Computer and Automation Institute, Hungarian Academy of Sciences, H-1111, Budapest, Kende u. 13-17, Hungary

    Zsolt Tuza

  2. Department of Computer Science, University of Pannonia, H-8200, Veszprém, Hungary

    Zsolt Tuza

  3. Department of Mathematics and Physics, Troy University, Troy, AL, 36082, USA

    Vitaly Voloshin

Authors
  1. Zsolt Tuza
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  2. Vitaly Voloshin
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Editors and Affiliations

  1. Alfréd Rényi Inst. of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Ervin Győri , Gyula O. H. Katona  & Gábor Sági ,  & 

  2. Institute of Mathematics, Eötvös University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary

    László Lovász

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© 2008 János Bolyai Mathematical Society and Springer-Verlag

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Tuza, Z., Voloshin, V. (2008). Problems and Results on Colorings of Mixed Hypergraphs. In: Győri, E., Katona, G.O.H., Lovász, L., Sági, G. (eds) Horizons of Combinatorics. Bolyai Society Mathematical Studies, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77200-2_12

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