JournalsqtVol. 4, No. 1pp. 77–90

Polynomial invariants of graphs on surfaces

  • Ross Askanazi

    The Ohio State University, Columbus, OH, USA
  • Sergei Chmutov

    The Ohio State University, Columbus, OH, USA
  • Charles Estill

    The Ohio State University, Columbus, OH, USA
  • Jonathan Michel

    The Ohio State University, Columbus, OH, USA
  • Patrick Stollenwerk

    The Ohio State University, Columbus, OH, USA
Polynomial invariants of graphs on surfaces cover
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Abstract

For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. This gives an expression of the polynomial, defined by M. Las Vergnas in a combinatorial way using matroids as a specialization of the Krushkal polynomial, defined using the symplectic structure in the first homology group of the surface.

Cite this article

Ross Askanazi, Sergei Chmutov, Charles Estill, Jonathan Michel, Patrick Stollenwerk, Polynomial invariants of graphs on surfaces. Quantum Topol. 4 (2013), no. 1, pp. 77–90

DOI 10.4171/QT/35