# Publications

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In preparation:

A.J. Goodall, F. Jouve, J.-S. Sereni, Galois groups of families of Tutte polynomials.

Submitted:

A.J. Goodall, F. Jouve, J.-S. Sereni, Vector spaces spanned by Tutte polynomials. 50pp. March 2024. Preprint hal-04485620

Journal publications:

A.J. Goodall, D. Garijo and L. Vena, Homomorphisms between graphs embedded on surfaces. European Journal of Combinatorics Volume 118, May 2024, 103936. Preprint arXiv:2305.03107 [math.CO].

I. Moffatt, J. Ellis-Monaghan, A.J. Goodall, S.D. Noble and L. Vena, Irreducibility of the Tutte polynomial of an embedded graph, Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1337--1351 doi: 10.5802/alco.252.

A.J. Goodall, B.M. Litjens, G. Regts and L. Vena, Tutte's dichromate for signed graphs, Discrete Appl. Math. 289 (2021), 153--184. doi: 10.1016/j.dam.2020.09.021. Preprint arXiv:1903.07548 [math.CO]

A.J. Goodall, B.M. Litjens, G. Regts and L. Vena, A Tutte polynomial for maps II: the non-orientable case. European J. Combin. 86 (2020), doi: 10.1016/j.ejc.2020.103095. Preprint arXiv:1804.01496 [math.CO]

A.J. Goodall, T. Krajewski, G. Regts and L. Vena, A Tutte polynomial for maps. Combin. Probab. Comput. 27:6 (2018), 913--945. Preprint arXiV:1610.04486 [math.CO], and IUUK-CE-ITI Series 649.

A.J. Goodall, M. Hermann, T. Kotek, J. A. Makowsky, S.D. Noble, On the complexity of generalized chromatic polynomials. Adv. Appl. Math. 94 (2017), 71--102. doi:10.1016/j.aam.2017.04.005 Preprint: arXiv:1701.06639 [math.CO] doi: 10.1016/j.aam.2017.04.005

A.J. Goodall, G. Regts and L. Vena, Matroid invariants and counting graph homomorphisms. Linear Algebra Appl. 494 (2016), 263--273. doi:10.1016/j.laa.2016.01.022 Preprint: arXiv:1512.01507 [math.CO]. Published version also at IUUK-CE-ITI Series 2016-637.

A.J. Goodall, J. Nešetřil and P. Ossona de Mendez, Strongly polynomial sequences as interpretations of trivial structures, J. Appl. Logic 18 (2016), 129--149. doi:10.1016/j.jal.2016.06.001 arXiv:1405.2449 [math.CO]. Published version also at IUUK-CE-ITI Series 2015-631.

D. Garijo, A.J. Goodall and J. Nešetřil, Polynomial graph invariants from homomorphism numbers, Discrete Math. 339 (2016), no. 4, 1315--1328. 10.1016/j.disc.2015.11.022. Preprint: arXiv: 1308.3999 [math.CO]. A poster produced for EuroComb 2013 in Pisa based on an early version of this paper.

D. Garijo, A.J. Goodall and J. Nešetřil, On the number of B-flows of a graph, European J. Combin. 35 (2014), 273-285. [ITI series version]

A.J. Goodall, C. Merino, A. de Mier, and M. Noy, On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1), Ann. Combin. 17:2 (2013), 311-332. [Preliminary version in Proceedings of FPSAC 2011, Reykjavik, Iceland: DMTCS proc. AO, (2011) 411-422. Pre-publication version.]

D. Garijo, A.J. Goodall and J. Nešetřil, Contractors for flows, Proc. Amer. Math. Soc. 141 (2013), 1849-1861. [ITI series version, arXiv version]

A.J. Goodall and A. de Mier, Spanning trees of 3-uniform hypergraphs, Adv. Appl. Math., 47:4 (2011), 840-868 [arXiv version]

A.J. Goodall, A. de Mier, S. Noble, and M. Noy, The Tutte polynomial characterizes simple outerplanar graphs, Combin. Probab. Comput. 20 (2011), 609-616. Preprint. [Also as a EuroComb 2011 paper, Electronic Notes Discrete Math. 38 (2011), 639-644.]

D. Garijo, A.J. Goodall and J. Nešetřil, Distinguishing graphs by left and right homomorphism profiles, European J. Combin. 32 (2011), 1025-1053 [KAM series version]

A.J. Goodall, Parity, Eulerian subgraphs and the Tutte polynomial, J. Combin. Theory Ser. B. 98: 3 (2008), 599-628. Preprint at arxiv: 0707.2306 [math.CO].

A.J. Goodall, Some new evaluations of the Tutte polynomial, J. Combin. Theory Ser. B. 96:2 (2006), 207-224. Preprint.

A.J. Goodall, The Tutte polynomial modulo a prime, Adv. Appl. Math. 32:1-2 (2004), 293-298. Preprint.

A.J. Goodall and D.J.A. Welsh, On the parity of colourings and flows, J. Comb. Theory B. 84:2 (2002), 364-365.

M. Bálek and A.J. Goodall, Book review - L. Lovász, Large Networks and Graph Limits, Computer Science Review 10 (2013), 35-46. Also IUUK-CE-ITI Series 2013-602.

Book chapters:

D. Garijo, A.J. Goodall and J. Nešetřil, Colorings and flows. In: J. Ellis-Monaghan and I. Moffatt, eds., Handbook of the Tutte Polynomial and Related Topics, Chapman and Hall/CRC Press, 2022.

D. Garijo, A.J. Goodall, J. Nešetřil and G. Regts, Polynomials and graph homomorphisms. In: J. Ellis-Monaghan and I. Moffatt, eds., Handbook of the Tutte Polynomial and Related Topics, Chapman and Hall/CRC Press, 2022.

A.J. Goodall, Fourier analysis on finite Abelian groups: some graphical applications. In: G. Grimmett and C. McDiarmid (eds.), Combinatorics, Complexity and Chance: a tribute to Dominic Welsh, OUP, 2007. pp. 103-129. Preprint.

Refereed conference proceedings:

A.J. Goodall, B. Litjens, G. Regts, and L. Vena. A Tutte polynomial for non-orientable maps. Eurocomb 2017 extended abstract. Electron. Notes Discrete Math. 61 (2017): 513-519.

D. Garijo, A.J. Goodall and J. Nešetřil, Polynomial graph invariants from homomorphism numbers. In: J. Nešetřil and M. Pellegrini (Eds.), The Seventh European Conference on Combinatorics, Graph Theory and Applications, Extended abstracts of Eurocomb 2013, Pisa, Italy. Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series 16. Pisa: Edizioni della Normale, 2013, pp. 611-12.

D. Garijo, A.J. Goodall and J. Nešetřil, Contractors for flows, Electron. Notes Discrete Math. 38 (2011), 389–394

D. Garijo, A.J. Goodall and J. Nešetřil, Graph homomorphisms, the Tutte polynomial and “q-state Potts uniqueness”, Electron. Notes Discrete Math. 34 (2009), 231-236.

A.J. Goodall, Graph polynomials and Tutte-Grothendieck invariants: an application of elementary finite Fourier analysis, in M. Klazar and M. Loebl (eds.), Enumeration Workshop, Patejdlova bouda, Špindlerův Mlýn, November 17-23, 2007, KAM-DIMATIA series 2008-899, Charles University, Prague, Czech Republic, September 2008. Available at arXiv:0806.4848 [math.CO]. 18pp.

Editorial:

A.J. Goodall, G. Hahn and J. Nešetřil (eds.), Claude Berge: Qui a tué le duc de Densmore? In preparation. Trilingual edition of IUUK-CE-ITI Series 2013-598 (English translations of articles in French prepared by J. Blin, A.J. Goodall, and G. Hahn.)

J. Ellis-Monaghan, A.J. Goodall, K. Morgan and I. Moffatt (eds.), Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401), Dagstuhl Reports 9: 9 (2020)

G A.J. Goodall and L. Vena (eds.), Structural Graph Theory, DocCourse 2014 Lecture Notes, IUUK-CE-ITI Series 651.

J. Ellis-Monaghan, A.J. Goodall, J.A. Makowsky and I. Moffatt (eds.), Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241), Dagstuhl Reports 6: 6 (2016)

T. Brazdil, A. Goodall, A. Kucera, P. Milstainova, J. Nesetril, H. Nesetrilova, J. Obdrzalek (eds.) Highlights of Logic, Games, and Automata (2015).

Preprints:

W. Prichard, A. Cobham and A.J. Goodall, The ICTD Government Revenue Dataset, ICTD Working Paper 19, September 2014. 62pp. (For more about this ICTD project see here.)

A.J. Goodall and S.D Noble, Counting cocircuits and convex two-colourings is #P-complete, October 2008, arXiv: 0810.2042 [math.CO]. 5pp. This paper has been incorporated into A.J. Goodall, M. Hermann, T. Kotek, J. A. Makowsky, S.D. Noble, On the complexity of generalized chromatic polynomials, Adv. Appl. Math., 2017 [see above].

A.J. Goodall, Edge colouring models for the Tutte polynomial and related graph invariants, May 2007, arxiv: 0707.2297 [math.CO]. 33pp.

Lecture notes:

A. J. Goodall, The Tutte polynomial and related polynomials: lecture notes 2010, 2012, 2014. (and as 2017-652 on CE-ITI series). Collected together from courses given as part of Selected Chapters in Combinatorics (Vybrane kapitoly z kombinatoriky I): ``Many facets of the Tutte polynomial" (2010), ``Graph invariants, homomorphisms and the Tutte polynomial" (2012), and ``Duality in combinatorics: the examples of Tutte, Erdos, and Ramsey" (2014).

Doctoral thesis:

A.J. Goodall, Graph polynomials and the discrete Fourier transform, D.Phil. thesis, University of Oxford, 2004 (126pp). (Contains material published in the articles "The Tutte polynomial modulo a prime" and "Some new evaluations of the Tutte polynomial," and, in developed form, in "Parity, Eulerian subgraphs and the Tutte polynomial," "Edge colouring models for the Tutte polynomial and related graph invariants," and the survey "Fourier analysis on finite Abelian groups: some graphical applications.")

Coauthors

Martin Bálek, Delia Garijo, Miki Hermann, Tomer Kotek, Thomas Krajewski, Bart Litjens, Janos Makowsky, Anna de Mier, Criel Merino, Jaroslav Nešetřil, Steve Noble, Marc Noy, Guus Regts, Lluís Vena Cros, Dominic Welsh

Slides from talks

Occasionally I succeed in having slides "I prepared earlier" rather than the more ephemeral medium of blackboard and chalk. Here are some:

2018 "A Tutte polynomial for maps" from work with T, Krajewski, B. Litjens, G. Regts and L. Vena (given as a talk at 27th Workshop Cycles and Colourings, High Tatras, Slovakia in September).

2016 "Graph polynomials and matroid invariants from graph homomorphisms" from work with J. Nešetřil, P. Ossona de Mendez, G. Regts and L. Vena (given as a talk at Technion, Haifa in January).

2015 "The Second Alaska Winter School in Combinatorics in Photographs" (17MB pdf file), presented at the John Gimbel Fest, Prague, 3-4 August: In March 2014 eight mathematicians wended their way to Byers Lake at the behest and conveyance of Professor John Gimbel. Although darkness obscures some of the memory of that Alaskan sojourn, there remains a body of photographs - taken by the speaker and by Jan Hubička - that bears witness to something having happened.

2015 An updated version of the talk Graph polynomials from simple graph sequences from work with D. Garijo, J. Nešetřil and P. Ossona de Mendez (given as a talk at Zámeček workshop, Hlohovec in March). Another, later one (RHUL Workshop on the Tutte polynomial in July).

2014 Graph polynomials from simple graph sequences. From work with D. Garijo, J. Nešetřil and P. Ossona de Mendez (drawing on the papers "Polynomial graph invariants from homomorphism numbers" and "Strongly polynomial sequences as interpretations of trivial structures").

2013 Polynomial graph invariants from graph homomorphisms. Based on the eponymous paper with D. Garijo and J. Nešetřil.

Other matters

Co-organizer with Jo Ellis-Monaghan, Iain Moffatt, and Kerri Morgan of Dagstuhl Seminar, 29 Sept -4 Oct 2019 - Comparative theory for graph polynomials

Co-organizer with Janos Makowsky and Elena Ravve (ORT Braude, Karmiel) of the LICS 2017 Workshop on Metafinite model theory and definability and complexity of numeric graph parameters on Monday 19 June 2017 at the Symposium on Logic in Computer Science in Reykjavik, Iceland, 20-23 June.

Co-organizer with Jo Ellis-Monaghan, Iain Moffatt, and Janos Makowsky of Dagstuhl Seminar, 12-17 June 2016 - Graph polynomials: towards a comparative theory

Organizing committee member for Highlights of Logic, Games and Automata, 15-18 September, 2015. Programme. (With J. Nešetřil, produced conference poster.)

From 9 October to 20 November 2014 the Doc-Course in Structural Graph Theory took place at IUUK/KAM, MFF, Charles University in Prague: five visitors to the department each gave a short series of lectures on topics from graph theory, constraint satisfaction problems and the interaction of combinatorics with logic and physics. Information leaflet. A booklet of notes derived from these lectures, edited by Lluís Vena Cros and Andrew Goodall, will appear in IUUK-CE-ITI Series.

Co-organizer with Jo Ellis-Monaghan and Janos Makowsky of the minisymposium "Graph Polynomials: Toward a General Theory" Parts I and II, SIAM Conference on Discrete Mathematics and its Applications, 17 & 19 June 2014, Minneapolis, Minnesota, USA