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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Contractors for flows


Authors: Delia Garijo, Andrew Goodall and Jaroslav Nešetřil
Journal: Proc. Amer. Math. Soc. 141 (2013), 1849-1861
MSC (2010): Primary 05C21, 05C25; Secondary 05C99
Published electronically: December 4, 2012
MathSciNet review: 3034412
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Abstract | References | Similar Articles | Additional Information

Abstract: We answer a question raised by Lovász and B. Szegedy [Contractors and connectors in graph algebras, J. Graph Theory 60:1 (2009)] asking for a contractor for the graph parameter counting the number of $ B$-flows of a graph, where $ B$ is a subset of a finite Abelian group closed under inverses. We prove our main result using the duality between flows and tensions and finite Fourier analysis.


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Additional Information

Delia Garijo
Affiliation: Department of Applied Mathematics I, University of Seville, Seville, Spain
Email: dgarijo@us.es

Andrew Goodall
Affiliation: Department of Applied Mathematics (KAM) and Institute of Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic
Email: goodall.aj@gmail.com

Jaroslav Nešetřil
Affiliation: Department of Applied Mathematics (KAM) and Institute of Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic
Email: nesetril@kam.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11449-2
Keywords: Graph homomorphism, Fourier transform, contractor, flows, tensions
Received by editor(s): January 13, 2011
Received by editor(s) in revised form: September 15, 2011
Published electronically: December 4, 2012
Additional Notes: The first author’s research supported by projects O.R.I MTM2008-05866-C03-01 and PAI FQM-0164
The second and third authors’ research supported by ITI 1M0545 and the Centre for Discrete Mathematics, Theoretical Computer Science and Applications (DIMATIA)
Communicated by: Jim Haglund
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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