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Selected publications by topic

A full list of publications, ordered by publication date, is also available.

Rota's Conjecture

• Solving Rota's Conjecture
  AMS Notices 2014, With Bert Gerards and Geoff Whittle
• On Rota's Conjecture and nested separations in matroids
  arXiv:1310.6990. With Shalev Ben-David.
• On Rota's Conjecture and excluded minors containing large projective geometries
  JCTb 2006. With Bert Gerards and Geoff Whittle
• The excluded minors for GF$(4)$-representable matroids
  JCTb 2000. With Bert Gerards and Ajai Kapoor

Inequivalent representations of matroids

• Inequivalent representations of matroids over prime fields
  AAM 2013. With Geoff Whittle
• 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

Growth rates of minor-closed classes

• Growth rates of minor-closed classes of matroids.
  JCTb 2009. With Joseph Kung and Geoff Whittle
• Projective geometries in dense matroids.
  JCTb 2008. With Kasper Kabell
• Cliques in dense GF$(q)$-representable matroids
  JCTb 2003. With Geoff Whittle
• The densest matroids in minor-closed classes with exponential growth rate,
  arXiv:1410.7676. With Peter Nelson.

Extremal matroid theory

• The critical number of dense triangle-free binary matroids,
  arXiv:1406.2588. With Peter Nelson.
• An analogue of the Erdos-Stone theorem for finite geometries
  Combinatorica 2015. With Peter Nelson.
• A Density Hales-Jewett Theorem for matroids
  JCTb 2015. With Peter Nelson.
• The Erdos-Posa property for matroid circuits.
  JCTb 2009. With Kasper Kabell

Branch-width for matroids

• Excluding a planar graph from GF$(q)$-representable matroids
  JCTb 2007. With Bert Gerards and Geoff Whittle
• Branch width and well-quasi-ordering in matroids and graphs
  JCTb 2002. With Bert Gerards and Geoff Whittle. Correction
• Branch-width and Rota's conjecture
  JCTb 2002. With Geoff Whittle
• On the excluded minors for the matroids of branch-width $k$
  JCTb 2003. With Bert Gerards, Neil Robertson, and Geoff Whittle

Matroid structure beyond finite fields

• Some open problems on excluding a uniform matroid.
  AAM 2008.
• Representation of matroids with a modular plane
  arXiv:1304.6448. With Rohan Kapadia.
• Representability of matroids with a large projective geometry minor
  JCTb 2015. With Rohan Kapadia.

Signed graphs and group-labelled graphs

• Excluding a group-labelled graph
  JCTb 2008. With Bert Gerards
• The odd-minor variant of Hadwiger's conjecture,
  JCTb 2009. With Bert Gerards, Bruce Reed, Paul Seymour, Adrian Vetta.
• Packing odd circuits into Eulerian graphs
  JCTb 2002. With Bertrand Guenin

Matchings and generalizations

• Packing non-zero $A$-paths in group-labelled graphs
  Combinatorica 2006. With Chudnovsky, Gerards, Goddyn, Lohman, and Seymour
• An algorithm for packing non-zero $A$-paths in group-labelled graphs
  Combinatorica 2008. With Maria Chudnovsky and Bill Cunningham
• An algebraic matching algorithm
  Combinatorica 2000.
• Matroid matching via mixed skew-symmetric matrices
  Combinatorica 2005. With Satoru Iwata

Matroid connectivity

• Matroid $3$-connectivity and branch width
  JCTb 2015. With Stefan van Zwam.
• Generating weakly $4$-connected matroids
  JCTb 2008. With Xaingqian Zhou
• Matroid $4$-connectivity: a deletion-contraction theorem
  JCTb 2001. With Geoff Whittle
• A splitter theorem for internally $4$-connected binary matroids
  SIAM J. Discrete Math 2006. With Xaingqian Zhou

Cute

• Characterizing graphic matroids by a system of linear equations
  JCTb 2013. With Bert Gerards.
• Straight line embeddings of planar graphs with integer edge lengths
  JGT 2008. With Anjie Guo and David McKinnon.