Note: Dual graph homomorphism functions

  • Authors:

  • László Lovász;Alexander Schrijver

  • Affiliations:

  • Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary;CWI and University of Amsterdam, Amsterdam, The Netherlands

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

For any two graphs F and G, let hom(F,G) denote the number of homomorphisms F-G, that is, adjacency preserving maps V(F)-V(G) (graphs may have loops but no multiple edges). We characterize graph parameters f for which there exists a graph F such that f(G)=hom(F,G) for each graph G. The result may be considered as a certain dual of a characterization of graph parameters of the form hom(.,H), given by Freedman, Lovasz and Schrijver [M. Freedman, L. Lovasz, A. Schrijver, Reflection positivity, rank connectivity, and homomorphisms of graphs, J. Amer. Math. Soc. 20 (2007) 37-51]. The conditions amount to the multiplicativity of f and to the positive semidefiniteness of certain matrices N(f,k).