Homotopy Type of Complexes of Graph Homomorphisms between Cycles

@article{Cukic2006HomotopyTO,
  title={Homotopy Type of Complexes of Graph Homomorphisms between Cycles},
  author={Sonja Lj. Cukic and Dmitry N. Kozlov},
  journal={Discrete \& Computational Geometry},
  year={2006},
  volume={36},
  pages={313-329}
}
  • S. Cukic, D. Kozlov
  • Published 2 August 2004
  • Mathematics
  • Discrete & Computational Geometry
In this paper we study the homotopy type of Hom(Cm,Cn), where Ck is the cyclic graph with k vertices. We enumerate connected components of Hom(Cm,Cn) and show that each such component is either homeomorphic to a point or homotopy equivalent to S1. Moreover, we prove that Hom(Cm,Ln) is either empty or is homotopy equivalent to the union of two points, where Ln is an n-string, i.e., a tree with n vertices and no branching points. 

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Sweden, current address: Department of Computer Science, Eidgenössische Technische Hochschule , Zürich, Switzerland E-mail address: sonja.cukic@inf.ethz

  • Sweden, current address: Department of Computer Science, Eidgenössische Technische Hochschule , Zürich, Switzerland E-mail address: sonja.cukic@inf.ethz