Prof Steven Noble

Overview
Overview
Biography
I obtained my first degree in mathematics in 1993 from the University of Oxford, where I was a member of New College. I was fortunate enough to be able to continue studying in Oxford for a DPhil on the Complexity of Graph Polynomials under the supervision of Dominic Welsh which I completed in 1997. Between 1996 and 1998, I had parttime teaching appointments in Oxford at New College and then at Merton, covering for faculty who were on sabbatical. In October 1998 I was appointed as a lecturer at Brunel University and promoted to senior lecturer in 2010. From summer 2012 to summer 2015, I was head of department of mathematics at Brunel. During my time at Brunel I was admissions tutor and level one coordinator for several years. I moved to Birkbeck as Sundstrom Reader in Mathematics in 2016.
Qualifications
 BA Mathematics, University of Oxford, 1993
 DPhil Mathematics, University of Oxford, 1997
 Fellow of the Higher Education Academy, 2017

Research
Research
Research interests
 Combinatorics
 Computational Complexity
 Deltamatroids
 Embedded Graphs
 Graph Polynomials
Research overview
My research is in combinatorics, particularly graph polynomials, which is a very broad area of mathematics with many beautiful problems still to be solved. I have also been interested in computational complexity and the frequency assignment problem. More recently I have worked on embedded graphs, deltamatroids and multimatroids, establishing results in each of these areas guided by intuition from the others, and exploring generalizations of the Tutte polynomial.
Research clusters and groups
Research projects
The critical group of a topological graph: an approach through deltamatroid theory.

Supervision and teaching
Supervision and teaching
Supervision
Teaching
Teaching modules
 Problems in Mathematics (BUEM009S6)
 Numbers, Proofs and Counting (BUEM096S4)
 Algebra 2 (BUEM101S5)
 Finite Mathematics (BUEM105S6)

Publications
Publications
Article
 EllisMonaghan, 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. 13371351. ISSN 25895486.
 Moffatt, Iain and Noble, Steven (2021) Topological graph theory through matroid theory. Newsletter of the London Mathematical Society 496, pp. 2933. ISSN 25163841.
 Edwards, K. and Noble, Steven (2019) The complexity of solutionfree sets of integers for general linear equations. Discrete Applied Mathematics 270, pp. 115133. ISSN 0166218X.
 Bonin, J. and Chun, C. and Noble, Steven (2019) The excluded 3minors for vfsafe deltamatroids. Advances in Applied Mathematics 126 (101909), ISSN 01968858.
 Bonin, J. and Chun, C. and Noble, Steven (2019) Deltamatroids as subsystems of sequences of Higgs lifts. Advances in Applied Mathematics 126 (101910), ISSN 01968858.
 Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R. (2019) Matroids, deltamatroids and embedded graphs. Journal of Combinatorial Theory, Series A 167, pp. 759. ISSN 00973165.
 Chun, C. and Chun, D. and Moss, T. and Noble, Steven (2018) The eExchange Basis Graph and Matroid connectedness. Discrete Mathematics 342 (3), pp. 723725. ISSN 0012365X.
 Chun, C. and Moffatt, I. and Noble, Steven and Rueckriemen, R. (2018) On the interplay between embedded graphs and deltamatroids. Proceedings of the London Mathematical Society 118 (3), pp. 675700. ISSN 00246115.
 Chun, C. and Hall, R. and Merino, C. and Moffatt, I. and Noble, Steven (2018) The structure of deltamatroids with width one twists. Electronic Journal of Combinatorics 25 (1), ISSN 10778926.
 Funk, Daryl and Mayhew, Dillon and Noble, Steven (2017) How many deltamatroids are there?. European Journal of Combinatorics 69, pp. 149158. ISSN 01956698.
 Chun, C. and Chun, D. and Noble, Steven (2017) Inductive tools for connected deltamatroids and multimatroids. European Journal of Combinatorics 63, pp. 5969. ISSN 01956698.
 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. 71102. ISSN 01968858.
 Chun, C. and Hall, R. and Merino, C. and Noble, Steven (2017) On zeros of the characteristic polynomial of matroids of bounded treewidth. European Journal of Combinatorics 60, pp. 1020. ISSN 01956698.
 Noble, Steven and Royle, G.F. (2014) The Merino–Welsh conjecture holds for series–parallel graphs. European Journal of Combinatorics 38, pp. 2435. ISSN 01956698.
 Merino, C. and Noble, Steven and RamírezIbáñez, M. and VillarroelFlores, R. (2012) On the structure of the hvector of a paving matroid. European Journal of Combinatorics 33 (8), pp. 17871799. ISSN 01956698.
 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. 13691375. ISSN 0166218X.
 Eggemann, N. and Noble, Steven (2012) The complexity of two graph orientation problems. Discrete Applied Mathematics 160 (45), pp. 513517. ISSN 0166218X.
 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. 639644. ISSN 15710653.
 Noble, Steven and Hansen, P. and Mladenović, N. (2011) Maximizing edgeratio is NPcomplete. Discrete Applied Mathematics 159 (18), pp. 22762280. ISSN 0166218X.
 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. 609616. ISSN 09635483.
 Eggemann, N. and Noble, Steven (2011) The clustering coefficient of a scalefree random graph. Discrete Applied Mathematics 159 (10), pp. 953965. ISSN 0166218X.
 ChávezLomelí, L.E. and Merino, C. and Noble, Steven and RamírezIbáñez, M. (2011) Some inequalities for the Tutte polynomial. European Journal of Combinatorics 32 (3), pp. 422433. ISSN 01956698.
 Eggemann, N. and Havet, F. and Noble, Steven (2010) kL(2,1)labelling for planar graphs is NPcomplete for k≥4. Discrete Applied Mathematics 158 (16), pp. 17771788. ISSN 0166218X.
 Eggemann, N. and Noble, Steven (2009) Minimizing the Oriented Diameter of a Planar Graph. Electronic Notes in Discrete Mathematics 34, pp. 267271. ISSN 15710653.
 Merino, C. and Noble, Steven (2009) The equivalence of Two Graph Polynomials and a Symmetric Function. Combinatorics, Probability and Computing 18 (4), pp. 601615. ISSN 09635483.
 Noble, Steven (2009) Evaluating a Weighted Graph Polynomial for Graphs of Bounded TreeWidth. The Electronic Journal of Combinatorics 16 (1), pp. R64. ISSN 10778926.
 Noble, Steven (2006) Evaluating the rank generating function of a graphic 2polymatroid. Combinatorics, Probability and Computing 15 (3), pp. 449461. ISSN 09635483.
 Koller, A.E. and Noble, Steven (2004) Domination analysis of greedy heuristics for the frequency assignment problem. Discrete Mathematics 275 (13), pp. 331338. ISSN 0012365X.
 Krasikov, I. and Noble, Steven (2004) Finding nexttoshortest paths in a graph. Information Processing Letters 92 (3), pp. 117119. ISSN 00200190.
 Leese, R.A. and Noble, Steven (2004) Cyclic labelling with constraints at two distances. The Electronic Journal of Combinatorics 11 (1), ISSN 10778926.
 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 10778926.
 Noble, Steven and Welsh, D.J.A. (2000) Knot graphs. Journal of Graph Theory 34 (1), pp. 100111. ISSN 03649024.
 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. 10571087. ISSN 03730956.
 Noble, Steven (1998) Evaluating the Tutte polynomial for graphs of bounded treewidth. Combinatorics, Probability and Computing 7 (3), pp. 307321. ISSN 09635483.
 Noble, Steven (1996) Recognising a partitionable simplicial complex is in NP. Discrete Mathematics 152 (13), pp. 303305. ISSN 0012365X.
Book Section
 Noble, Steven (2022) The U, V and W polynomials. In: EllisMonaghan, 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. 191212. ISBN 9780198571278.
Monograph
 Knapp, C. and Noble, Steven (2022) The complexity of the Greedoid Tutte Polynomial. London, UK: Birkbeck, University of London.
 EllisMonaghan, 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. London, UK: Birkbeck, University of London.
 Bonin, J.E. and Chun, C. and Noble, Steven (2018) Deltamatroids as subsystems of sequences of Higgs Lifts. London, UK: Birkbeck, University of London.
 Bonin, J.E. and Chun, C. and Noble, Steven (2018) The excluded 3minors for Vfsafe Deltamatroids. London, UK: Birkbeck, University of London.
 Chun, C. and Hall, R. and Merino, C. and Moffatt, I. and Noble, Steven (2017) The structure of Deltamatroids with Width One Twists. London, UK: Birkbeck, University of London.
 Goodall, A. and Hermann, M. and Kotek, T. and Makowsky, J.A. and Noble, Steven (2017) On the complexity of Generalized Chromatic Polynomials. London, UK: Birkbeck, University of London.
 Funk, D. and Mayhew, D. and Noble, Steven (2016) How many deltamatroids are there?. London, UK: Birkbeck, University of London.
 Chun, C. and Hall, R. and Merino, C. and Noble, Steven (2016) On zeros of the characteristic polynomial of matroids of bounded treewidth. London, UK: Birkbeck, University of London.
 Chun, C. and Chun, D. and Noble, Steven (2016) Inductive tools for connected ribbon graphs, deltamatroids and multimatroids. London, UK: Birkbeck, University of London.
Other
 Noble, Steven (2017) C++ code referred to in Funk, Mayhew, Noble, "How many deltamatroids are there?".