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Nowhere-Zero \({\vec{k}}\)-Flows on Graphs

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Abstract

We introduce and study a multivariate function that counts nowhere-zero flows on a graph G, in which each edge of G has an individual capacity. We prove that the associated counting function is a piecewise-defined polynomial in these capacities, which satisfies a combinatorial reciprocity law that incorporates totally cyclic orientations of G.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, San Francisco, CA, 94132, USA

    Matthias Beck

  2. Department of Mathematics, Trinity College, Hartford, CT, 06106, USA

    Alyssa Cuyjet

  3. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA

    Gordon Rojas Kirby

  4. Department of Mathematics, University of Oklahoma, Norman, OK, 73071, USA

    Molly Stubblefield

  5. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Michael Young

Authors
  1. Matthias Beck
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  2. Alyssa Cuyjet
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  3. Gordon Rojas Kirby
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  4. Molly Stubblefield
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  5. Michael Young
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Correspondence to Matthias Beck.

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Beck, M., Cuyjet, A., Kirby, G.R. et al. Nowhere-Zero \({\vec{k}}\)-Flows on Graphs. Ann. Comb. 18, 579–583 (2014). https://doi.org/10.1007/s00026-014-0246-5

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  • DOI: https://doi.org/10.1007/s00026-014-0246-5

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