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**48**.

## Article

Ellis-Monaghan, J. and Goodall, A. and Moffatt, I. and Noble, Steven and Vena, L.
(2022)
Irreducibility of the Tutte polynomial of an embedded graph.
*Algebraic Combinatorics* 5
(6),
pp. 1337-1351.
ISSN 2589-5486.

Moffatt, Iain and Noble, Steven
(2021)
Topological graph theory through matroid theory.
*Newsletter of the London Mathematical Society* 496
,
pp. 29-33.
ISSN 2516-3841.

Edwards, K. and Noble, Steven
(2019)
The complexity of solution-free sets of integers for general
linear equations.
*Discrete Applied Mathematics* 270
,
pp. 115-133.
ISSN 0166-218X.

Bonin, J. and Chun, C. and Noble, Steven
(2019)
The excluded 3-minors for vf-safe delta-matroids.
*Advances in Applied Mathematics* 126
(101909),
ISSN 0196-8858.

Bonin, J. and Chun, C. and Noble, Steven
(2019)
Delta-matroids as subsystems of sequences of Higgs lifts.
*Advances in Applied Mathematics* 126
(101910),
ISSN 0196-8858.

Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R.
(2019)
Matroids, delta-matroids and embedded graphs.
*Journal of Combinatorial Theory, Series A* 167
,
pp. 7-59.
ISSN 0097-3165.

Chun, C. and Chun, D. and Moss, T. and Noble, Steven
(2018)
The e-Exchange Basis Graph and Matroid connectedness.
*Discrete Mathematics* 342
(3),
pp. 723-725.
ISSN 0012-365X.

Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R.
(2018)
On the interplay between embedded graphs and delta-matroids.
*Proceedings of the London Mathematical Society* 118
(3),
pp. 675-700.
ISSN 0024-6115.

Chun, C. and Hall, R. and Merino, C. and Moffatt, I. and Noble, Steven
(2018)
The structure of delta-matroids with width one twists.
*Electronic Journal of Combinatorics* 25
(1),
ISSN 1077-8926.

Funk, Daryl and Mayhew, Dillon and Noble, Steven
(2017)
How many delta-matroids are there?
*European Journal of Combinatorics* 69
,
pp. 149-158.
ISSN 0195-6698.

Chun, C. and Chun, D. and Noble, Steven
(2017)
Inductive tools for connected delta-matroids and multimatroids.
*European Journal of Combinatorics* 63
,
pp. 59-69.
ISSN 0195-6698.

Goodall, A. and Hermann, M. and Kotek, T. and Makowsky, J.A. and Noble, Steven
(2017)
On the complexity of generalized chromatic polynomials.
*Advances in Applied Mathematics* 94
,
pp. 71-102.
ISSN 0196-8858.

Chun, C. and Hall, R. and Merino, C. and Noble, Steven
(2017)
On zeros of the characteristic polynomial of matroids of bounded tree-width.
*European Journal of Combinatorics* 60
,
pp. 10-20.
ISSN 0195-6698.

Noble, Steven and Royle, G.F.
(2014)
The Merino–Welsh conjecture holds for series–parallel graphs.
*European Journal of Combinatorics* 38
,
pp. 24-35.
ISSN 0195-6698.

Merino, C. and Noble, Steven and Ramírez-Ibáñez, M. and Villarroel-Flores, R.
(2012)
On the structure of the h-vector of a paving matroid.
*European Journal of Combinatorics* 33
(8),
pp. 1787-1799.
ISSN 0195-6698.

Lin, Y. and Noble, Steven and Jin, X. and Cheng, W.
(2012)
On plane graphs with link component number equal to the nullity.
*Discrete Applied Mathematics* 160
(9),
pp. 1369-1375.
ISSN 0166-218X.

Eggemann, N. and Noble, Steven
(2012)
The complexity of two graph orientation problems.
*Discrete Applied Mathematics* 160
(4-5),
pp. 513-517.
ISSN 0166-218X.

Goodall, A.J. and de Mier, A. and Noble, Steven and Noy, M.
(2011)
The Tutte polynomial characterizes simple outerplanar graphs.
*Electronic Notes in Discrete Mathematics* 38
,
pp. 639-644.
ISSN 1571-0653.

Noble, Steven and Hansen, P. and Mladenović, N.
(2011)
Maximizing edge-ratio is NP-complete.
*Discrete Applied Mathematics* 159
(18),
pp. 2276-2280.
ISSN 0166-218X.

Goodall, A.J. and de Mier, A. and Noble, Steven and Noy, M.
(2011)
The Tutte Polynomial characterizes simple outerplanar graphs.
*Combinatorics, Probability and Computing* 20
(4),
pp. 609-616.
ISSN 0963-5483.

Eggemann, N. and Noble, Steven
(2011)
The clustering coefficient of a scale-free random graph.
*Discrete Applied Mathematics* 159
(10),
pp. 953-965.
ISSN 0166-218X.

Chávez-Lomelí, L.E. and Merino, C. and Noble, Steven and Ramírez-Ibáñez, M.
(2011)
Some inequalities for the Tutte polynomial.
*European Journal of Combinatorics* 32
(3),
pp. 422-433.
ISSN 0195-6698.

Eggemann, N. and Havet, F. and Noble, Steven
(2010)
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4.
*Discrete Applied Mathematics* 158
(16),
pp. 1777-1788.
ISSN 0166-218X.

Eggemann, N. and Noble, Steven
(2009)
Minimizing the Oriented Diameter of a Planar Graph.
*Electronic Notes in Discrete Mathematics* 34
,
pp. 267-271.
ISSN 1571-0653.

Merino, C. and Noble, Steven
(2009)
The equivalence of Two Graph Polynomials and a Symmetric Function.
*Combinatorics, Probability and Computing* 18
(4),
pp. 601-615.
ISSN 0963-5483.

Noble, Steven
(2009)
Evaluating a Weighted Graph Polynomial for Graphs of Bounded Tree-Width.
*The Electronic Journal of Combinatorics* 16
(1),
R64.
ISSN 1077-8926.

Noble, Steven
(2006)
Evaluating the rank generating function of a graphic 2-polymatroid.
*Combinatorics, Probability and Computing* 15
(3),
pp. 449-461.
ISSN 0963-5483.

Leese, R.A. and Noble, Steven
(2004)
Cyclic labelling with constraints at two distances.
*The Electronic Journal of Combinatorics* 11
(1),
ISSN 1077-8926.

Koller, A.E. and Noble, Steven
(2004)
Domination analysis of greedy heuristics for the frequency assignment problem.
*Discrete Mathematics* 275
(1-3),
pp. 331-338.
ISSN 0012-365X.

Krasikov, I. and Noble, Steven
(2004)
Finding next-to-shortest paths in a graph.
*Information Processing Letters* 92
(3),
pp. 117-119.
ISSN 0020-0190.

Calkin, N. and Merino, C. and Noble, Steven and Noy, M.
(2003)
Improved bounds for the number of forests and acyclic orientations in the square lattice.
*The Electronic Journal of Combinatorics* 10
,
ISSN 1077-8926.

Noble, Steven and Welsh, D.J.A.
(2000)
Knot graphs.
*Journal of Graph Theory* 34
(1),
pp. 100-111.
ISSN 0364-9024.

Noble, Steven and Welsh, D.J.A.
(1999)
A weighted graph polynomial from chromatic invariants of knots.
*Annales de l'Institut Fourier* 49
(3),
pp. 1057-1087.
ISSN 0373-0956.

Noble, Steven
(1998)
Evaluating the Tutte polynomial for graphs of bounded tree-width.
*Combinatorics, Probability and Computing* 7
(3),
pp. 307-321.
ISSN 0963-5483.

Noble, Steven
(1996)
Recognising a partitionable simplicial complex is in NP.
*Discrete Mathematics* 152
(1-3),
pp. 303-305.
ISSN 0012-365X.

## Book Section

Noble, Steven
(2022)
The U, V and W polynomials.
In:
Ellis-Monaghan, J.A. and Moffatt, I. (eds.)
*Handbook of the Tutte Polynomial and Related Topics.*
Chapman & Hall.
ISBN 9781482240627.

Noble, Steven
(2007)
Complexity of graph polynomials.
In:
McDiarmid, C.J.H. and Grimmett, G.R. (eds.)
*Combinatorics, Complexity and Chance: A Tribute to Dominic Welsh.*
Oxford, UK:
Oxford University Press.
ISBN 9780198571278.

Noble, Steven
(2007)
Complexity of graph polynomials.
In:
Grimmett, G. and McDiarmid, C. (eds.)
*Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh.*
Oxford Academic, pp. 191-212.
ISBN 9780198571278.

## Monograph

Knapp, C. and Noble, Steven (2022) The complexity of the Greedoid Tutte Polynomial. Technical Report. Birkbeck, University of London, London, UK. (Submitted)

Ellis-Monaghan, Jo.A. and Goodall, A.J. and Moffatt, I. and Noble, Steven and Vena, L. (2021) Irreducibility of the Tutte polynomial of an embedded graph. Technical Report. Birkbeck, University of London, London, UK. (Submitted)

Bonin, J.E. and Chun, C. and Noble, Steven (2018) Delta-matroids as subsystems of sequences of Higgs Lifts. Technical Report. Birkbeck, University of London, London, UK.

Bonin, J.E. and Chun, C. and Noble, Steven (2018) The excluded 3-minors for Vf-safe Delta-matroids. Technical Report. Birkbeck, University of London, London, UK.

Chun, C. and Hall, R. and Merino, C. and Moffatt, I. and Noble, Steven (2017) The structure of Delta-matroids with Width One Twists. Technical Report. Birkbeck, University of London, London, UK.

Goodall, A. and Hermann, M. and Kotek, T. and Makowsky, J.A. and Noble, Steven (2017) On the complexity of Generalized Chromatic Polynomials. Technical Report. Birkbeck, University of London, London, UK.

Funk, D. and Mayhew, D. and Noble, Steven (2016) How many delta-matroids are there? Technical Report. Birkbeck, University of London, London, UK.

Chun, C. and Hall, R. and Merino, C. and Noble, Steven (2016) On zeros of the characteristic polynomial of matroids of bounded tree-width. Technical Report. Birkbeck, University of London, London, UK.

Chun, C. and Chun, D. and Noble, Steven (2016) Inductive tools for connected ribbon graphs, delta-matroids and multimatroids. Technical Report. Birkbeck, University of London, London, UK.

## Other

Noble, Steven (2017) C++ code referred to in Funk, Mayhew, Noble, "How many delta-matroids are there?". UNSPECIFIED. (Unpublished)