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Contractors and connectors of graph algebras
Article first published online: 6 OCT 2008
DOI: 10.1002/jgt.20343
Copyright © 2008 Wiley Periodicals, Inc.
1097-0118/asset/cover.gif?v=1&s=747ee645df081de59c78864878c8bdb9daeca9a1 "Journal of Graph Theory")
Additional Information
How to Cite
Lovász, L. and Szegedy, B. (2009), Contractors and connectors of graph algebras. Journal of Graph Theory, 60: 11–30. doi: 10.1002/jgt.20343
Publication History
- Issue published online: 11 NOV 2008
- Article first published online: 6 OCT 2008
- Manuscript Revised: 20 JUN 2008
- Manuscript Received: 25 MAY 2005
Funded by
- OTKA. Grant Number: 67867
- Abstract
- References
- Cited By
Keywords:
- graph homomorphism;
- graph algebra;
- contractor;
- connector
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