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Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401)

Authors Jo Ellis-Monaghan, Andrew Goodall, Iain Moffatt, Kerri Morgan and all authors of the abstracts in this report



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Jo Ellis-Monaghan
Andrew Goodall
Iain Moffatt
Kerri Morgan
and all authors of the abstracts in this report

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Jo Ellis-Monaghan, Andrew Goodall, Iain Moffatt, and Kerri Morgan. Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401). In Dagstuhl Reports, Volume 9, Issue 9, pp. 135-155, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/DagRep.9.9.135

Abstract

This report documents the programme and outcomes of Dagstuhl Seminar 19401 ``Comparative Theory for Graph Polynomials''. The study of graph polynomials has become increasingly active, with new applications and new graph polynomials being discovered each year. The genera of graph polynomials are diverse, and their interconnections are rich. Experts in the field are finding that proof techniques and results established in one area can be successfully extended to others. From this a general theory is emerging that encapsulates the deeper interconnections between families of graph polynomials and the various techniques, computational approaches, and methodologies applied to them. The overarching aim of this Seminar was to exploit commonalities among polynomial invariants of graphs, matroids, and related combinatorial structures. Model-theoretic, computational and other methods were used in order to initiate a comparative theory that collects the current state of knowledge into a more cohesive and powerful framework.
Keywords
  • graph polynomials
  • graph and matroid invariants
  • Tutte polynomial
  • topological and algebraic graph theory

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