HOMOMORPHISMS OF TREES INTO A PATH.

Let hom(G, H) denote the number of homomorphisms from a graph G to a graph H. In this paper we study the number of homomorphisms of trees into a path, and prove that hom(Pm, Pn) ≤ hom(Tm, Pn) ≤ hom(Sm, Pn), where Tm is any tree on m vertices, and Pm and Sm denote the path and star on m vertices, respectively. This completes the study of extremal problems concerning the number of homomorphisms between trees started in the paper Graph Homomorphisms Between Trees [Electron. J. Combin., 21 (2014), 4.9] written by the authors of the current paper. [ABSTRACT FROM AUTHOR]