Abstract
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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Cukic, S., Kozlov, D. Homotopy Type of Complexes of Graph Homomorphisms between Cycles. Discrete Comput Geom 36, 313–329 (2006). https://doi.org/10.1007/s00454-006-1245-z
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DOI: https://doi.org/10.1007/s00454-006-1245-z