Geoff Whittle's Publications

This page lists some of my research publications. The files provided for download are mostly preprints, with the corresponding final versions being available at the given doi's.

Preprints

• Certifying non-representability of matroids over prime fields (with Jim Geelen),
  Submitted pdf
• Excluding Kuratowski graphs and their duals from binary matroids (with Dillon Mayhew and Gordon Royle),
  Submitted pdf

2014

Solving Rota's Conjecture (with Jim Geelen and Bert Gerards),
Notices of the AMS 61 (2014) 736–743 pdf, doi: 10.1090/noti1139

Intertwining connectivity in matroids (with Rong Chen),
SIAM J. Discrete Math. 28-3 (2014) 1402–1404 pdf, doi: 10.1137/140959626

Is the missing axiom of matroid theory lost forever? (with Dillon Mayhew and Mike Newman),
Quart. J. Math. 65 (2014) 1397–1415 pdf, doi: 10.1093/qmath/hat031

2013

• Structure in minor-closed classes of matroids (with Jim Geelen and Bert Gerards),
  in Surveys in Combinatorics 2013 (Simon Blackburn, Stefanie Gerke and Mark Wildon eds.) London Mathematical Society Lecture Notes Series 409 Cambridge University Press, Cambridge pdf
• Inequivalent representations of matroids over prime fields (with Jim Geelen),
  Advances in Applied Math. 51 (2013) 1–175 pdf, doi: 10.1016/j.aam.2013.02.001
• On maintaining 3-connectivity relative to a fixed basis (with Alan Williams),
  European Journal of Combinatorics 34 (2013) 957–967 pdf, doi: 10.1016/j.ejc.2013.02.001
• Tangles, trees and flowers (with Ben Clark),
  J. Combin. Theory Ser. B 103 (2013) 385–407 pdf, doi: 10.1016/j.jctb.2013.03.002

2012

• The structure of graphs with a vital linkage of order 2 (with Dillon Mayhew and Stefan van Zwam),
  Journal of Graph Theory 71 (2012) 176–181, pdf, doi: 10.1002/jgt.20640
• Stability, fragility, and Rota's Conjecture (with Dillon Mayhew and Stefan van Zwam),
  J. Combin. Theory Ser. B 102 (2012) 760–783, pdf, doi: 10.1016/j.jctb.2011.09.004
• An upgraded wheels and whirls theorem for 3-connected matroids (with James Oxley and Charles Semple),
  J. Combin. Theory Ser. B 102 (2012) 610–637, pdf, doi: 10.1016/j.jctb.2011.09.005
• Capturing matroid elements in unavoidable 3-connected minors (with Deborah Chun and James Oxley),
  European Journal of Combinatorics 33 (2012) 1100–1112, pdf, doi: 10.1016/j.ejc.2012.01.012

2011

• Exposing 3-separations in 3-connected matroids (with James Oxley and Charles Semple),
  Advances in Applied Mathematics 47 (2011) 463–508, pdf, doi: 10.1016/j.aam.2010.10.009
• The excluded minors for the class of matroids that are either binary or ternary (with Dillon Mayhew, Bogdan Oporowski and James Oxley),
  European Journal of Combinatorics 32 (2011) 891–930, pdf, doi: 10.1016/j.ejc.2011.01.017
• On the asymptotic proportion of connected matroids (with Dillon Mayhew, Mike Newman and Dominic Welsh),
  European Journal of Combinatorics 32 (2011) 882–890, pdf, doi: 10.1016/j.ejc.2011.01.016
• An obstacle to a decomposition theorem for near-regular matroids (with Dillon Mayhew and Stefan van Zwam),
  SIAM J. Discrete Math 25 (2011) 271–279, pdf, doi: 10.1137/090759616

2010

• The Internally 4-Connected Binary Matroids with no M(K_3,3)-minor (with Dillon Mayhew and Gordon Royle),
  Mem. Am. Math. Soc. 208 (2010) no. 981, pdf, doi: 10.1090/S0065-9266-10-00600-9
• On inequivalent representations of matroids over non-prime fields (with Jim Geelen and Bert Gerards),
  J. Combin. Theory Ser. B 100 (2010) 740–743, pdf, doi: 10.1016/j.jctb.2010.08.001
• The projective plane is a stabilizer (with Jim Geelen),
  J. Combin. Theory Ser. B 100 (2010) 128–131, pdf, doi: 10.1016/j.jctb.2009.05.002

2009

• Addendum to matroid tree-width (with Petr Hliněný),
  Eur. J. Combin.30 (2009), 1036–1044 pdf, doi: 10.1016/j.ejc.2008.09.028
• On excluded minors for real-representability (with Dillon Mayhew and Mike Newman),
  J. Combin. Theory B 99 (2009) 685–689, pdf, doi: 10.1016/j.jctb.2008.12.003
• Tangles, tree-decompositions and grids in matroids (with Jim Geelen and Bert Gerards),
  J. Comb. Theory B 99 (2009) 657–667, pdf, doi: 10.1016/j.jctb.2007.10.008
• Growth rates of minor-closed classes of matroids (with Jim Geelen and Joseph Kung),
  J. Comb. Theory B 99 (2009) 420–427, pdf, doi: 10.1016/j.jctb.2008.08.006

2008

• Maintaining 3-connectivity relative to a fixed basis (with James Oxley and Charles Semple),
  Adv. Appl. Math. 41 (2008) 1–9, doi: 10.1016/j.aam.2007.05.001
• A chain theorem for matroids (with James Oxley and Charles Semple),
  J. Comb. Theory B 98 (2008) 447–483, doi: 10.1016/j.jctb.2007.08.005
• Wild triangles in 3-connected matroids (with James Oxley and Charles Semple),
  J. Comb. Theory B 98 (2008) 291–323, doi: 10.1016/j.jctb.2007.06.004 See pdf for a version that corrects a small error in the original.

2007

• Excluding a planar graph from GF(q)-representable matroids (with Jim Geelen and Bert Gerards),
  J. Comb. Theory B 97 (2007) 971–998, doi: 10.1016/j.jctb.2007.02.005
• Towards a structure theory for matrices and matroids (with Jim Geelen and Bert Gerards).
  In: Proceedings of the International Congress of Mathematicians, Madrid 2006 (Marta Sanz-Solé, Javier Soria, Juan Luis Varona and Joan Verdera eds.), vol. 3 (2007), Eur. Math. Soc., pdf
• The structure of the 3-separations of 3-connected matroids II (with James Oxley and Charles Semple),
  Eur. J. Combin. 28 (2007) 1239–1261, doi: 10.1016/j.ejc.2006.01.007
• Towards a matroid minor structure theory (with Jim Geelen and Bert Gerards).
  In: Combinatorics, Complexity and Chance: A Tribute to Dominic Welsh (Geoffrey Grimmett and Colin McDiarmid eds.), Oxford Lecture Series in Mathematics and its Applications 34 (2007) 72–82, Oxford University Press, Oxford. pdf

2006

• Matroid tree-width (with Petr Hliněný),
  Eur. J. Combin. 27 (2006) 1117–1128, doi: 10.1016/j.ejc.2006.06.005
• Matroid T-Connectivity (with Jim Geelen and Bert Gerards),
  SIAM J. Discrete Math. 20 (2006) 588–596, pdf, doi: 10.1137/050634190
• Obstructions to branch-decompositions of matroids (with J. Geelen, B. Gerards and N. Robertson),
  J. Comb. Theory B 96 (2006) 560–570, doi: 10.1016/j.jctb.2005.11.001
• A correction to our paper "Branch-width and well-quasi-ordering in matroids and graphs" (with Jim Geelen and Bert Gerards),
  Manuscript, Jun 2006 pdf
• On Rota's conjecture and excluded minors containing large projective geometries (with Jim Geelen and Bert Gerards),
  J. Comb. Theory B 96 (2006) 405–425, doi: 10.1016/j.jctb.2005.09.005

2005

• Recent work in matroid representation theory,
  Discrete Math. 302 (2005) 285–296, doi: 10.1016/j.disc.2004.07.039

2004

• The structure of the 3-separations of 3-connected matroids (with James Oxley and Charles Semple),
  J. Comb. Theory B 96 (2004) 257–293, doi: 10.1016/j.jctb.2004.03.006
• Inequivalent representations of matroids having no U_3,6-minor (with Jim Geelen and Dillon Mayhew),
  J. Comb. Theory B 92 (2004) 55–67, doi: 10.1016/j.jctb.2003.12.005
• Bridging Separations in Matroids (with Jim Geelen and Petr Hliněný),
  SIAM J. Discrete Math. 18 (2004) 638–646, doi: 10.1137/S089548010139638X
• A short proof of non-GF(5)-representability of matroids (with Jim Geelen, James Oxley and Dirk Vertigan),
  J. Comb. Theory B 91 (2004) 105–121, doi: 10.1016/j.jctb.2003.11.001
• Fork-decompositions of matroids (with Rhiannon Hall, James Oxley and Charles Semple),
  Adv. Appl. Math. 32 (2004) 523–575, doi: 10.1016/S0196-8858(03)00058-7

2003

• On the excluded minors for the matroids of branch-width k (with J. F. Geelen, A. M. H. Gerards and N. Robertson),
  J. Comb. Theory B 88 (2003) 261–265, doi: 10.1016/S0095-8956(02)00046-1
• Disjoint cocircuits in matroids with large rank (with James F. Geelen and A. M. H. Gerards),
  J. Comb. Theory B 87 (2003) 270–279, doi: 10.1016/S0095-8956(02)00010-2
• Cliques in dense GF(q)-representable matroids (with James Geelen),
  J. Comb. Theory B 87 (2003) 264–269, doi: 10.1016/S0095-8956(02)00009-6

2002

• Branch-Width and Rota's Conjecture (with James Geelen),
  J. Comb. Theory B 86 (2002) 315–330, doi: 10.1006/jctb.2002.2130
• On Matroids of Branch-Width Three (with Rhiannon Hall, James Oxley and Charles Semple),
  J. Comb. Theory B 86 (2002) 148–171, doi: 10.1006/jctb.2002.2120
• Branch-Width and Well-Quasi-Ordering in Matroids and Graphs (with James F. Geelen and A. M. H. Gerards),
  J. Comb. Theory B 84 (2002) 270–290, doi: 10.1006/jctb.2001.2082
• Infinite antichains of matroids with characteristic set {p} (with James Oxley, Charles Semple and Dirk Vertigan),
  Discrete Math. 242 (2002) 175–185, doi: 10.1016/S0012-365X(00)00466-0
• Totally Free Expansions of Matroids (with James Geelen, James Oxley and Dirk Vertigan),
  J. Comb. Theory B 84 (2002) 130–179, doi: 10.1006/jctb.2001.2068

2001

• Matroid 4-Connectivity: A Deletion-Contraction Theorem (with James Geelen),
  J. Comb. Theory B 83 (2001) 15–37, doi: 10.1006/jctb.2001.2032

2000

• On the non-uniqueness of q-cones of matroids (with James Oxley),
  Discrete Math. 218 (2000) 271–275, doi: 10.1016/S0012-365X(99)00358-1
• On the Excluded Minors for Quaternary Matroids (with J. F. Geelen, J. G. Oxley and D. L. Vertigan),
  J. Comb. Theory B 80 (2000) 57–68, doi: 10.1006/jctb.2000.1967

1999

• Arrangements, Channel Assignments and Associated Polynomials (with Dominic J. A. Welsh),
  Adv. Appl. Math. 23 (1999) 375–406, doi: 10.1006/aama.1999.0660
• Stabilizers of Classes of Representable Matroids,
  J. Comb. Theory B 77 (1999) 39–72, doi: 10.1006/jctb.1999.1908
• The Parameterized Complexity of Some Fundamental Problems in Coding Theory (with Rod G. Downey, Michael R. Fellows and Alexander Vardy),
  SIAM J. Comput. 29 (1999) 545–570, doi: 10.1137/S0097539797323571

1998

• Weak Maps and Stabilizers of Classes of Matroids (with James Geelen, James Oxley and Dirk Vertigan),
  Adv. Appl. Math. 21 (1998) 305–341, doi: 10.1006/aama.1998.0600, pdf
• On Maximum-Sized Near-Regular and ⁶√1-Matroids (with James Oxley and Dirk Vertigan),
  Graph Combinator. 14 (1998) 163–179, doi: 10.1007/s003730050024, pdf
• On Weak Maps of Ternary Matroids (with James Oxley),
  Eur. J. Combin. 19 (1998) 377–389, doi: 10.1006/eujc.1997.0180, pdf

1997

• A 2-Isomorphism Theorem for Hypergraphs (with Dirk Vertigan),
  J. Comb. Theory B 71 (1997) 215–230, doi: 10.1006/jctb.1997.1789, pdf
• On Matroids Representable Over GF(3) and Other Fields,
  T. Am. Math. Soc. 349 (1997) 579–603, Stable URL: http://www.jstor.org/stable/2155388

Selected Earlier Publications

• On Representable Matroids having Neither U_2,5- Nor U_3,5-minors (with Charles Semple).
  In: Matroid Theory: AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory July 2–6, 1995, University of Washington, Seattle (Joseph E. Bonin, James G. Oxley and Brigitte Servatius eds.), Contemporary Mathematics 197 (1996) 377–386, Am. Math. Soc., Providence, RI. pdf
• On Inequivalent Representations of Matroids over Finite Fields (with James Oxley and Dirk Vertigan),
  J. Comb. Theory B 67 (1996) 325–343, doi: 10.1006/jctb.1996.0049, pdf
• Partial Fields and Matroid Representation (with Charles Semple),
  Adv. Appl. Math. 17 (1996) 184–208, doi: 10.1006/aama.1996.0010, pdf
• A Characterization of the Matroids Representable over GF(3) and the Rationals,
  J. Comb. Theory B 65 (1995) 222–261, doi: 10.1006/jctb.1995.1052, pdf
• The Critical Problem for Polymatroids,
  Q. J. Math. 45 (1994) 117–125, doi: 10.1093/qmath/45.1.117, pdf
• Recognizing Polymatroids Associated with Hypergraphs (with Dirk Vertigan),
  Comb. Probab. Comput. 2 (1993) 519–530, pdf
• A Characterization of Tutte Invariants of 2-Poymatroids (with J. Oxley),
  J. Comb. Theory B 59 (1993) 210–244, doi: 10.1006/jctb.1993.1067, pdf
• Tutte invariants for 2-polymatroids (with James Oxley).
  In: Graph Structure Theory: Proceedings of a AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors Held June 22 to July 5, 1991 at the University of Washington, Seattle (Neil Robertson and Paul Seymour eds.), Contemporary Mathematics 147 (1993) 9–20, Am. Math. Soc., Providence, RI. pdf
• Characteristic Polynomials of Weighted Lattices,
  Adv. Math. 99 (1993) 125–151, doi: 10.1006/aima.1993.1021, pdf
• Dowling group geometries and the critical problem,
  J. Comb. Theory B 47 (1989) 80–92, doi: 10.1016/0095-8956(89)90067-1, pdf
• q-Lifts of Tangential k-Blocks,
  J. London Math. Soc. 39 (1989) 9–15, doi: 10.1112/jlms/s2-39.1.9, pdf
• Quotients of Tangential k-Blocks,
  P. Am. Math. Soc. 102 (1988) 1088–1098, Stable URL: http://www.jstor.org/stable/2047362
• Modularity of tangential k-blocks,
  J. Comb. Theory B 42 (1987) 24–35, doi: 10.1016/0095-8956(87)90060-8, pdf
• On the critical exponent of transversal matroids,
  J. Comb. Theory B 37 (1984) 94–95, doi: 10.1016/0095-8956(84)90049-2, pdf