Contractors and connectors of graph algebras

  • Authors:

  • László Lovász;Balázs Szegedy

  • Affiliations:

  • Eötvös Loránd University, Budapest, Hungary H-1518, PF 120;University Of Toronto, 40 George St. Toronto, Ontario, Canada M5S 2E4

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2009

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Abstract

We study generalizations of the “contraction-deletion” relation of the Tutte polynomial, and other similar simple operations, to other graph parameters. The question can be set in the framework of graph algebras introduced by Freedman at al [Reflection positivity, rank connectivity, and homomorphisms of graphs, J. Amer. Math. Soc. 20 (2007), 37–51.] Graph algebras are defined by a graph parameter, and they were introduced in order to study and characterize homomorphism functions. We prove that for homomorphism functions, these graph algebras have special elements called “contractors” and “connectors”. This gives a new characterization of homomorphism functions. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 11–30, 2009