## Publications

- K. J. Edwards, S. D. Noble. The complexity of solution-free sets of integers. Under review. ArXiv
- J. E. Bonin, C. Chun, S. D. Noble. The excluded 3-minors for vf-safe delta-matroids.
*Advances in Applied Mathematics*In Press. ArXiv - J. E. Bonin, C. Chun, S. D. Noble. Delta-matroids as subsystems of sequences of Higgs lifts.
*Advances in Applied Mathematics*In Press. ArXiv - C. Chun, D. Chun, T. Moss, S. D. Noble. e-exchange basis graph and matroid connectedness.
*Discrete Mathematics***342**(2019) 723-725. - C. Chun, R. Hall, C. Merino, I. Moffatt, S. D. Noble. The structure of delta-matroids with width one twists.
*The Electronic Journal of Combinatorics***25**(2018) P1.9. Electronic Journal of Combinatorics - D. Funk, D. Mayhew, S. D. Noble. How many delta-matroids are there?
*European Journal of Combinatorics***69**(2018) 149-158. ArXiv - A. J. Goodall, M. Hermann, T. Kotek, J. A. Makowsky, S. D. Noble. On the complexity of generalized chromatic polynomials.
*Advances in Applied Mathematics***94**(2018) 71-102. ArXiv - C. Chun, I. Moffatt, S. D. Noble, R. Rueckriemen. Matroids, delta-matroids and embedded graphs.
*Journal of Combinatorial Theory A***167**(2019) 7-59. ArXiv - C. Chun, I. Moffatt, S. D. Noble, R. Rueckriemen. On the interplay between embedded graphs and delta-matroids.
*Proceedings of the London Mathematical Society***118**(2019) 675-700. ArXiv - S. D.Noble. The U, V and W polynomials. Invited chapter for
*CRC Handbook on the Tutte Polynomial*, editors J. Ellis-Monaghan, I. Moffatt. - C. Chun, D. Chun, S. D. Noble. Inductive tools for connected delta-matroids and multimatroids.
*European Journal of Combinatorics***63**(2017) 59-69. ArXiv - C. Chun, R. M.Hall, C. Merino, S. D. Noble. On zeros of the characteristic polynomial of matroids of bounded tree-width.
*European Journal of Combinatorics***60**(2017) 10-20. ArXiv - S. D. Noble, G. F. Royle. The Merino-Welsh conjecture holds for series-parallel graphs.
*European Journal of Combinatorics***38**(2014) 24-35. ArXiv - C. Merino, S. D. Noble, M. Ramírez-Ibañez and R. Villarroel. On the structure of the h-vector of a paving matroid.
*European Journal of Combinatorics***33**(2012) 1787-1799. ArXiv - Y. Lin, S. D. Noble, X. Jin and W. Cheng. On plane graphs with link component number equal to the nullity.
*Discrete Applied Mathematics***160**(2012) 1369-1375. - N. Eggemann and S. D. Noble. The complexity of two graph orientation problems.
*Discrete Applied Mathematics***160**(2012) 513-517. ArXiv - S. D. Noble, P. Hansen and N. Mladenović. Maximizing edge-ratio is NP-complete.
*Discrete Applied Mathematics***159**(2011) 2276-2280. Brunel University Research Archive - A. J. Goodall, A. de Mier, S. D. Noble and M. Noy. The Tutte polynomial characterizes simple outerplanar graphs.
*Combinatorics Probability and Computing***20**(2011) 609-616. Brunel University Research Archive - L. Chávez-Lomelí, C. Merino, S. D. Noble and M. Ramírez-Ibañez. Some inequalities for the Tutte polynomial.
*European Journal of Combinatorics***32**(2011) 422-433. ArXiv - A. J. Goodall, A. de Mier, S. D. Noble and M. Noy. The Tutte polynomial characterizes simple outerplanar graphs.
*Electronic Notes in Discrete Mathematics***38**(2011) 639-644. - N. Eggemann and S. D. Noble. The clustering coefficient of a scale-free random graph.
*Discrete Applied Mathematics***159**(2011) 953-965. ArXiv - N. Eggemann, F. Havet and S. D. Noble. k-L(2,1)-labelling for planar graphs is NP-complete for k ≥ 4.
*Discrete Applied Mathematics***158**(2010) 1777-1788. ArXiv - N. Eggemann and S. D. Noble. Minimizing the oriented diameter of a planar graph.
*Electronic Notes in Discrete Mathematics***34**(2009) 267-271. Brunel University Research Archive - C. Merino and S. D. Noble. The equivalence of two graph polynomials and a symmetric function.
*Combinatorics Probability and Computing***18**(2009) 601-615. ArXiv - S. D. Noble. Evaluating a weighted graph polynomial for graphs of bounded tree-width.
*The Electronic Journal of Combinatorics***16**(2009) R64. Electronic Journal of Combinatorics - S. D. Noble. Complexity of graph polynomials. In Combinatorics, Complexity and Chance - A Tribute to Dominic Welsh eds C. J. H. McDiarmid and G. R. Grimmett. Oxford University Press (2007).
- S. D. Noble. Evaluating the rank generating function of a graphic 2-polymatroid.
*Combinatorics, Probability and Computing***15**(2006) 449-461. Brunel University Research Archive - I. Krasikov and S. D. Noble. Finding next-to-shortest paths in a graph. Information Processing Letters
**92**(2004) 117-119. Brunel University Research Archive - R. A. Leese and S. D. Noble. Cyclic labelling with constraints at two distances.
*Electronic Journal of Combinatorics*.**11**(2004) R10. Electronic Journal of Combinatorics - A. E. Koller and S. D. Noble. The domination number of greedy heuristics for the frequency assignment problem.
*Discrete Mathematics***275**(2004) 331-338. Brunel University Research Archive - N. Calkin, C. Merino, S. D. Noble and M. Noy. Improved bounds for the number of forests and acyclic orientations in the square lattice.
*Electronic Journal of Combinatorics***10**(2003) R4. Electronic Journal of Combinatorics - M. J. Luczak and S. D. Noble. Optimal arrangement of data in a tree directory.
*Discrete Applied Mathematics***121**(2002) 307-315. Brunel University Research Archive - S. D. Noble and D. J. A. Welsh. Knot graphs.
*Journal of Graph***34**(2000) 100-111. Brunel University Research Archive - S. D. Noble and D. J. A. Welsh. A weighted graph polynomial from Vassiliev invariants.
*Annales de l'Institut Fourier***49**(1999) 1057-1087. - S. D. Noble. Evaluating the Tutte polynomial for graphs of bounded tree-width.
*Combinatorics, Probability and Computing***7**(1998) 307-323. Brunel University Research Archive - S. D. Noble. Recognising a partitionable simplicial complex is in NP.
*Discrete Mathematics***152**(1996) 303-305. Brunel University Research Archive