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All publications

Submitted

• Naji's characterization of circle graphs
  arXiv:1801.03263. With Edward Lee.
• Matroid fragility and relaxations of circuit hyperplanes
  arXiv:1801.03263. With Florian Hoersch.
• On the complex-representable excluded minors for real-representability
  arXiv:1801.08656. With Rutger Campbell.
• A generalization of the Grid Theorem
  arXiv:1609.09098. With Benson Joeris.
• Representation of matroids with a modular plane
  arXiv:1304.6448. With Rohan Kapadia.

Published

• Infinitely many excluded minors for frame matroids and for lifted-graphic matroids
  JCTb 2018. With Rong Chen.
• Explicit bounds for graph minors
  JCTb 2018. With Tony Huynh, R. Bruce Richter
• Improved bounds for Rota's Basis Conjecture,
  Combinatorica, accepted. With Sally Dong.
• The structure of matroids with a spanning clique or projective geometry,
  JCTb 2017., With Peter Nelson.
• The densest matroids in minor-closed classes with exponential growth rate,
  Trans. Amer. Math. Soc., 2017. With Peter Nelson.
• Quasi-graphic matroids,
  JGT 2017. With Bert Gerards and Geoff Whittle.
• Computing girth and cogirth in perturbed graphic matroids,
  Combinatorica 2017. With Rohan Kapadia.
• On Rota's Conjecture and nested separations in matroids
  JCTb 2016. With Shalev Ben-David.
• The critical number of dense triangle-free binary matroids,
  JCTb 2016. With Peter Nelson.
• Certifying Non-representability of Matroids Over Prime Fields
  JCTb 2016. With Geoff Whittle
• Odd circuits in dense binary matroids,
  Combinatorica 2015. With Peter Nelson.
• The number of lines in a matroid with no $U_{2,n}$-minor
  European J. Combin. 2015. With Peter Nelson
• Projective geometries in exponentially dense matroids. I
  JCTb 2015. With Peter Nelson
• Matroid $3$-connectivity and branch width
  JCTb 2015. With Stefan van Zwam.
• A Density Hales-Jewett Theorem for matroids
  JCTb 2015. With Peter Nelson.
• Representability of matroids with a large projective geometry minor
  JCTb 2015. With Rohan Kapadia.
• Matroids denser than a clique,
  JCTb 2015. With Peter Nelson.
• The highly-connected matroids in minor-closed classes,
  Annals of Combinatorics 2015. With Bert Gerards and Geoff Whittle.
• Solving Rota's Conjecture
  AMS Notices 2014, With Bert Gerards and Geoff Whittle
• An analogue of the Erdos-Stone theorem for finite geometries
  Combinatorica 2014. With Peter Nelson.
• A geometric version of the Andrasfai-Erdos-Sos theorem,
  AAM 2014
• Inequivalent representations of matroids over prime fields
  AAM 2013. With Geoff Whittle
• Characterizing graphic matroids by a system of linear equations
  JCTb 2013. With Bert Gerards.
• On minor-closed classes of matroids with exponential growth rate
  AAM 2013. With Peter Nelson
• Structure in minor-closed classes of matroids.
  Surveys in Combinatorics 2013. With Bert Gerards, Geoff Whittle
• Small cocircuits in matroids
  European J. Combin. 2011.
• On inequivalent representations of matroids over non-prime fields
  JCTb 2010. With Bert Gerards and Geoff Whittle
• The projective plane is a stabilizer.
  JCTb 2010. With Geoff Whittle
• The number of points in a matroid with no $n$-point line as a minor.
  JCTb 2010. With Peter Nelson
• Circle graph obstructions under pivoting.
  JGTb 2009. With Sang-il Oum.
• Tangles, tree-decompositions, and grids in matroids
  JCTb 2009. With Bert Gerards and Geoff Whittle
• Growth rates of minor-closed classes of matroids.
  JCTb 2009. With Joseph Kung and Geoff Whittle
• The Erdos-Posa property for matroid circuits.
  JCTb 2009. With Kasper Kabell
• The odd-minor variant of Hadwiger's conjecture,
  JCTb 2009. With Bert Gerards, Bruce Reed, Paul Seymour, Adrian Vetta.
• Projective geometries in dense matroids.
  JCTb 2008. With Kasper Kabell
• Some open problems on excluding a uniform matroid.
  AAM 2008.
• Excluding a group-labelled graph
  JCTb 2008. With Bert Gerards
• An algorithm for packing non-zero $A$-paths in group-labelled graphs
  Combinatorica 2008. With Maria Chudnovsky and Bill Cunningham
• Generating weakly $4$-connected matroids
  JCTb 2008. With Xaingqian Zhou
• Straight line embeddings of planar graphs with integer edge lengths
  JGT 2008. With Anjie Guo and David McKinnon.
• Excluding a planar graph from GF$(q)$-representable matroids
  JCTb 2007. With Bert Gerards and Geoff Whittle
• On integer programming and the branch-width of the constraint matrix
  IPCO 2007, With Bill Cunningham
• On Rota's Conjecture and excluded minors containing large projective geometries
  JCTb 2006. With Bert Gerards and Geoff Whittle
• Packing non-zero $A$-paths in group-labelled graphs
  Combinatorica 2006. With Chudnovsky, Gerards, Goddyn, Lohman, and Seymour
• A splitter theorem for internally $4$-connected matroids
  SIDMA 2006. With Xaingqian Zhou
• Obstructions to branch-decomposition of matroids
  JCTb 2006. With Bert Gerards, Neil Robertson, and Geoff Whittle
• Matroid T-connectivity
  SIDMA 2006. With Bert Gerards and Geoff Whittle
• Matroid matching via mixed skew-symmetric matrices
  Combinatorica 2005. With Satoru Iwata
• Regular matroid decomposition via signed graphs
  JGT 2005. With Bert Gerards
• Bridging separations in matroids
  SIDMA 2005. With Petr Hlineny and Geoff Whittle
• A short proof of non-GF$(5)$-representability of matroids
  JCTb 2004. With James Oxley, Dirk Vertigan and Geoff Whittle
• Inequivalent representations of matroids having no $U_{3,6}$-minor
  JCTb 2004. With Dillon Mayhew and Geoff Whittle
• Embedding grids in surfaces
  European J. Combin. 2004. With Bruce Richter, Gelasio Salazar
• Cliques in dense GF$(q)$-representable matroids
  JCTb 2003. With Geoff Whittle
• Disjoint cocircuits in matroids with large rank
  JCTb 2003. With Bert Gerards and Geoff Whittle
• On the excluded minors for the matroids of branch-width $k$
  JCTb 2003. With Bert Gerards, Neil Robertson, and Geoff Whittle
• The linear delta-matroid parity problem
  JCTb 2003. With Satoru Iwata and Kazuo Murota.
• Branch-width and Rota's conjecture
  JCTb 2002. With Geoff Whittle
• Branch width and well-quasi-ordering in matroids and graphs
  JCTb 2002. With Bert Gerards and Geoff Whittle. Correction
• Packing odd circuits into Eulerian graphs
  JCTb 2002. With Bertrand Guenin
• Totally free expansions of matroids
  JCTb 2002. With James Oxley, Dirk Vertigan and Geoff Whittle
• Matroid $4$-connectivity: a deletion-contraction theorem
  JCTb 2001. With Geoff Whittle
• The excluded minors for GF$(4)$-representable matroids
  JCTb 2000. With Bert Gerards and Ajai Kapoor
• An algebraic matching algorithm
  Combinatorica 2000.
• On the excluded minors for quaternary matroids
  JCTb 2000. With James Oxley, Dirk Vertigan and Geoff Whittle
• On matroids without a non-Fano minor
  Discrete Math. 1999.
• Weak Maps and Stabilizers of Classes of Matroids
  AAM 1998. With James Oxley, Dirk Vertigan, Geoff Whittle
• Principally unimodular skew-symmetric matrices
  Combinatorica 1998. With Andre Bouchet and Bill Cunningham.
• Integral solutions of linear complementarity problems
  Math. OR. 1998. With Bill Cunningham.
• The optimal path-matching problem
  Combinatorica 1997. With Bill Cunningham.
• A Generalization of Tutte's Characterization of Totally Unimodular Matrices
  JCTb 1997.
• A two-dimensional Steinhaus theorem.
  Australas. J. Combin. 1993. With Jamie Simpson.

Not submitted for publication

• Colouring graphs with no odd-$K_n$ minor. With Tony Huynh. 2002
• On Tutte's paper "How to draw a graph". 2012
• Lectures on jump systems. 1996
• Matching Theory. EIDMA minicourse. 2001
• An algebraic approach to matching problems. 2001
• My PhD dissertation: Matchings, matroids and unimodular matrices 1995