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Decomposition of the Flow Polynomial

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Abstract

The flow polynomials denote the number of nowhere-zero flows on graphs, and are related to the well-known Tutte polynomials and chromatic polynomials. We will show the decomposition of the flow polynomials by edge-cuts and vertex-cuts of size 2 or 3. Moreover by using this decomposition, we will consider what kind of graphs have the same flow polynomials. Another application of the decomposition results is that if a bridgeless graph G does not admit a nowhere-zero k-flow and G has a small vertex- or edge-cut, then a proper bridgeless subgraph of G (a graph minor) does not admit a nowhere-zero k-flow either.

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Authors and Affiliations

  1. Department of Information Science, University of Tokyo, Tokyo, 113, Japan

    K. Sekine

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26506-63 10, USA

    C. Q. Zhang

Authors
  1. K. Sekine
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  2. C. Q. Zhang
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Sekine, K., Zhang, C.Q. Decomposition of the Flow Polynomial. Graphs and Combinatorics 13, 189–196 (1997). https://doi.org/10.1007/BF03352995

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  • DOI: https://doi.org/10.1007/BF03352995

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