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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Contractors for flows
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by Delia Garijo, Andrew Goodall and Jaroslav Nešetřil PDF
Proc. Amer. Math. Soc. 141 (2013), 1849-1861 Request permission

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.
References
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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
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1849-1861
  • MSC (2010): Primary 05C21, 05C25; Secondary 05C99
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11449-2
  • MathSciNet review: 3034412