Homomorphisms to oriented cycles

Abstract

We discuss the existence of homomorphisms to oriented cycles and give, for a special class of cyclesC, a characterization of those digraphs that admit, a homomorphism toC. Our result can be used to prove the multiplicativity of a certain class of oriented cycles, (and thus complete the characterization of multiplicative oriented cycles), as well as to prove the membership of the corresponding decision problem in the classNPϒcoNP. We also mention a conjecture on the existence of homomorphisms to arbitrary oriented cycles.

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Hell, P., Zhou, H. & Zhu, X. Homomorphisms to oriented cycles. Combinatorica 13, 421–433 (1993). https://doi.org/10.1007/BF01303514

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AMS subject classification code (1991)

  • 05 C 20
  • 05 C 99