Homomorphisms of Trees into a Path

• Main Authors: Csikvari, Peter (Contributor), Lin, Zhicong (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics, 2015-12-28T23:48:23Z.
• Subjects: Article
• Online Access: Get fulltext

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(P[subscript m],P[subscript n]) ≤ hom(T[subscript m],P[subscript n]) ≤ hom(S[subscript m],P[subscript n]), where T[subscript m] is any tree on m vertices, and P[subscript m] and S[subscript m] 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.