Abstract
A mixed hypergraph is a hypergraph with edges classified as of type 1 or type 2. A vertex coloring is strict if no edge of type 1 is totally multicolored, and no edge of type 2 monochromatic. The chromatic spectrum of a mixed hypergraph is the set of integers k for which there exists a strict coloring using exactly k different colors. A mixed hypertree is a mixed hypergraph in which every hyperedge induces a subtree of the given underlying tree. We prove that mixed hypertrees have continuous spectra (unlike general hypergraphs, whose spectra may contain gaps [cf. Jiang et al.: The chromatic spectrum of mixed hypergraphs, submitted]. We prove that determining the upper chromatic number (the maximum of the spectrum) of mixed hypertrees is NP-hard, and we identify several polynomially solvable classes of instances of the problem.
Research supported in part by Czech Research Grant GaČR 201/1999/0242.
This author acknowledges partial support of Czech research grants GAUK 158/1999 and KONTAKT 338/99. Part of the research was carried on while visiting Technical University Dresden in June 1999 and University of Oregon in the fall of 1999.
Research supported in part by National Science Foundation grants NSF-INT- 9802416 and NSF-ANI-9977524.
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© 2000 Springer-Verlag Berlin Heidelberg
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Král’, D., Kratochvíl, J., Proskurowski, A., Voss, HJ. (2000). Coloring Mixed Hypertrees. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_26
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DOI: https://doi.org/10.1007/3-540-40064-8_26
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