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Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401)

Authors: Jo Ellis-Monaghan, Andrew Goodall, Iain Moffatt, and Kerri Morgan

Published in: Dagstuhl Reports, Volume 9, Issue 9 (2020)

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.

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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)

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@Article{ellismonaghan_et_al:DagRep.9.9.135,
  author =	{Ellis-Monaghan, Jo and Goodall, Andrew and Moffatt, Iain and Morgan, Kerri},
  title =	{{Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401)}},
  pages =	{135--155},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{9},
  editor =	{Ellis-Monaghan, Jo and Goodall, Andrew and Moffatt, Iain and Morgan, Kerri},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.9.135},
  URN =		{urn:nbn:de:0030-drops-118460},
  doi =		{10.4230/DagRep.9.9.135},
  annote =	{Keywords: graph polynomials, graph and matroid invariants, Tutte polynomial, topological and algebraic graph theory}
}

Document

DOI: 10.4230/DagRep.6.6.26

Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241)

Authors: Jo Ellis-Monaghan, Andrew Goodall, Johann A. Makowsky, and Iain Moffatt

Published in: Dagstuhl Reports, Volume 6, Issue 6 (2016)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 16241 "Graph Polynomials: Towards a Comparative Theory". The area of graph polynomials has become in recent years incredibly active, with new applications and new graph polynomials being discovered each year. However, the resulting plethora of techniques and results now urgently requires synthesis. Beyond catalogues and classifications we need a comparative theory. The intent of this 5-day Seminar was to further a general theory of graph polynomials.

Cite as

Jo Ellis-Monaghan, Andrew Goodall, Johann A. Makowsky, and Iain Moffatt. Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241). In Dagstuhl Reports, Volume 6, Issue 6, pp. 26-48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{ellismonaghan_et_al:DagRep.6.6.26,
  author =	{Ellis-Monaghan, Jo and Goodall, Andrew and Makowsky, Johann A. and Moffatt, Iain},
  title =	{{Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241)}},
  pages =	{26--48},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{6},
  editor =	{Ellis-Monaghan, Jo and Goodall, Andrew and Makowsky, Johann A. and Moffatt, Iain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.6.26},
  URN =		{urn:nbn:de:0030-drops-67266},
  doi =		{10.4230/DagRep.6.6.26},
  annote =	{Keywords: complexity, counting functions, graph colourings, graph homomorphisms, graph invariants, graph polynomials, matroid invariants, second order logic, topological graph theory}
}

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Documents authored by Ellis-Monaghan, Jo

Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401)

Abstract

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Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241)

Abstract

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