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Complexity of Pattern Coloring of Cycle Systems

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Graph-Theoretic Concepts in Computer Science (WG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

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Abstract

A k-cycle system is a system of cyclically ordered k-tuples of a finite set. A pattern is a sequence of letters. A coloring of a k-cycle system with respect to a set of patterns of length k is proper iff each cycle is colored consistently with one of the patterns, i.e. the same/distinct letters correspond to the same/distinct color(s). We prove a dichotomy result on the complexity of coloring a given cycle system with a fixed set of patterns P by at most l colors and discuss possible generalizations.

The research was done as a part of DIMACS/DIMATIA REU 2001 programme. The REU programme was supported by KONTAKT ME 337.

Supported by Ministry of Education of Czech Republic as project LN00A056.

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Dvořák, Z., Kára, J., Král', D., Pangrác, O. (2002). Complexity of Pattern Coloring of Cycle Systems. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_15

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  • DOI: https://doi.org/10.1007/3-540-36379-3_15

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  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

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