Dual graph homomorphism functions

László Lovász, Alexander Schrijver

Research output: Contribution to journalArticle

2 Citations (Scopus)


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, Lovász and Schrijver [M. Freedman, L. Lovász, 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).

Original languageEnglish
Pages (from-to)216-222
Number of pages7
JournalJournal of Combinatorial Theory. Series A
Issue number2
Publication statusPublished - Feb 1 2010



  • Graph algebra
  • Graph homomorphism
  • Graph parameter
  • Positive semidefinite
  • Quantum graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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