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Publications

This page contains links to most of my publications. Some others can be found on the arxiv.

Submitted

• Monadic transductions and definable classes of matroids
  With Susan Jowett, Songbao Mo, and Christopher Tuffley.

Appeared

• Reduced clique graphs: a correction to "Chordal graphs and their clique graphs"
  With Andrew Probert.
  Graphs and Combinatorics 40 (2024) no. 58.
• Supersolvable saturated matroids and chordal graphs
  With Andrew Probert.
  Adv. in Appl. Math. 153 (2024) Article 102616.
• Tree automata and pigeonhole classes of matroids: II
  With Daryl Funk and Mike Newman.
  Electron. J. Combin. 30 (2023), no. 3, Paper #P3.6.
• Tree automata and pigeonhole classes of matroids: I
  With Daryl Funk and Mike Newman.
  Algorithmica. 84 (2022) 1795–1834.
• Defining bicircular matroids in monadic logic
  With Daryl Funk and Mike Newman.
  Q. J. Math. 73 (2022), no. 1, 65-92.
• Obstructions for bounded branch-depth in matroids
  With J. Pascal Gollin, Kevin Hendrey, and Sang-Il Oum.
  Advances in Combinatorics. https://doi.org/10.19086/aic.24227.
• Fractal classes of matroids
  With Mike Newman and Geoff Whittle.
  Adv. in Appl. Math. 126 (2021) Article 101995.
• Excluded minors for the class of split matroids
  With Amanda Cameron.
  Australas. J. Combin 79 (2021), no. 2, 195-204.
• The unbreakable frame matroids
  With Tara Fife, James Oxley, and Charles Semple.
  SIAM J. Discrete Math. 34 (2020), no. 3, 1522-1537.
• Effective versions of two theorems of Rado
  With Jason Bell, Daryl Funk, and Byoung Du Kim.
  Q. J. Math. 71 (2020), no. 2, 599-618.
• Structure of cubic Lehman matrices
  With Irene Pivotto and Gordon Royle.
  Electron. J. Combin. 26 (2019), no. 3, Paper #P3.54.
• Yes, the "missing axiom" of matroid theory is lost forever
  With Mike Newman and Geoff Whittle.
  Trans. Amer. Math. Soc. 370 (2018), no. 8, 5907-5929.
• On excluded minors for classes of graphical matroids
  With Daryl Funk.
  Discrete Math. 341 (2018), no. 6, 1509-1522.
• How many delta-matroids are there?
  With Daryl Funk and Steven Noble.
  European J. Combin. 69 (2018) 149-158.
• Excluding Kuratowski graphs and their duals from binary matroids
  With Gordon Royle and Geoff Whittle.
  J. Comb. Theory, Ser. B 125 (2017) 95-113.
• Towards a splitter theorem for internally 4-connected binary matroids IX: the theorem
  With Carolyn Chun and James Oxley.
  J. Comb. Theory, Ser. B 121 (2016) 2-67.
• Towards a splitter theorem for internally 4-connected binary matroids VIII: small matroids
  With Carolyn Chun and James Oxley.
  Adv. in Appl. Math. 85 (2017), 12-30.
• Unavoidable connected matroids retaining a specified minor
  With Carolyn Chun, Guoli Ding, and James Oxley.
  SIAM. J. Discrete Math. 30 (2016), no. 3, 1590-1606.
• The structure of {U25,U35}-fragile matroids
  With Ben Clark, Geoff Whittle, and Stefan van Zwam.
  SIAM. J. Discrete Math. 30 (2016), no. 3, 1480-1508.
• Fan-extensions in fragile matroids
  With Carolyn Chun, Deborah Chun, and Stefan van Zwam.
  Electron. J. Combin. 22 (2015), no. 2, Paper #P2.30.
• Obstacles to decomposition theorems for sixth-root-of-unity matroids
  With Carolyn Chun and Mike Newman.
  Ann. Comb. 19 (2015), no. 1, 79-93.
• Is the missing axiom of matroid theory lost forever?
  With Mike Newman and Geoff Whittle.
  Q. J. Math. 65 (2014), no. 4, 1397-1415.
• Maximum size binary matroids with no AG(3,2)-minor are graphic
  With Joseph Kung, Irene Pivotto, and Gordon Royle.
  SIAM J. Discrete Math. 28 (2014), no. 3, 1559-1577.
• Towards a splitter theorem for internally 4-connected binary matroids V
  With Carolyn Chun and James Oxley.
  Adv. in Appl. Math. 52 (2014), no. 1, 60-81.
• Towards a splitter theorem for internally 4-connected binary matroids IV
  With Carolyn Chun and James Oxley.
  Adv. in Appl. Math. 52 (2014), no. 1, 1-59.
• Towards a splitter theorem for internally 4-connected binary matroids III
  With Carolyn Chun and James Oxley.
  Adv. in Appl. Math. 51 (2013), no. 2, 309-344.
• Towards a splitter theorem for internally 4-connected binary matroids II
  With Carolyn Chun and James Oxley.
  European J. Combin. 36 (2014) 550-563.
• Constructing internally 4-connected binary matroids
  With Carolyn Chun and James Oxley.
  Adv. in Appl. Math. 50 (2013), no. 1, 16-45.
• On the number of sparse paving matroids
  With Dominic Welsh.
  Adv. in Appl. Math. 50 (2013), no. 1, 125-131.
• On the relative importance of excluded minors
  With Rhiannon Hall and Stefan van Zwam.
  Adv. in Appl. Math. 50 (2013), no. 1, 228-242.
• The structure of graphs with a vital linkage of order 2
  With Geoff Whittle and Stefan van Zwam.
  J. Graph Theory 71 (2012), no. 2, 176-181.
• The internally 4-connected binary matroids with no M(K5\e)-minor
  With Gordon Royle.
  SIAM J. Discrete Math. 26 (2012), no. 2, 755-767.
• Stability, fragility, and Rota's conjecture
  With Geoff Whittle and Stefan van Zwam.
  J. Comb. Theory, Ser. B 102 (2012), no. 3, 760-783.
• Towards a splitter theorem for internally 4-connected binary matroids
  With Carolyn Chun and James Oxley.
  J. Comb. Theory, Ser. B 102 (2012), no. 3, 688-700.
• The excluded minors for the class of matroids that are binary or ternary
  With Bogdan Oporowski, James Oxley, and Geoff Whittle.
  European J. Combin. 32 (2011), no. 6, 891-930.
• On the asymptotic proportion of connected matroids
  With Mike Newman, Dominic Welsh, and Geoff Whittle.
  European J. Combin. 32 (2011), no. 6, 882-890.
• The excluded minors for near-regular matroids
  With Rhiannon Hall and Stefan van Zwam.
  European J. Combin. 32 (2011), no. 6, 802-830.
• A chain theorem for internally 4-connected binary matroids
  With Carolyn Chun and James Oxley.
  J. Combin. Theory, Ser. B 101 (2011), no. 3, 141-189.
• An obstacle to a decomposition theorem for near-regular matroids
  With Geoff Whittle and Stefan van Zwam.
  SIAM J. Discrete Math. 25 (2011), no. 1, 271-279.
• The internally 4-connected binary matroids with no M(K3,3)-minor
  With Gordon Royle and Geoff Whittle.
  Memoirs of the AMS, 208 (2010), no. 981.
• On excluded minors for real-representability
  With Mike Newman and Geoff Whittle.
  J. Combin. Theory, Ser. B 99 (2009), no. 4, 685-689.
• Contracting an element from a cocircuit
  With Rhiannon Hall.
  Adv. in Appl. Math. 41 (2008), no. 4, 510-529.
• Matroids with nine elements
  With Gordon Royle.
  J. Combin. Theory, Ser. B 98 (2008), no. 2, 415-431.
• Matroid complexity and nonsuccinct descriptions
  SIAM J. Discrete Math. 22 (2008), no. 2, 455-466.
• Circuits and cocircuits in regular matroids
  Graphs Combin. 22 (2006), no. 3, 383-389.
• Equitable matroids
  Electron. J. Combin. 13 (2006), no. 1, Research Paper 41.
• Inequivalent representations of bias matroids
  Combin. Probab. Comput. 14 (2005), no. 4, 567-583.
• Families of matroids induced by classes of graphs
  Adv. in Appl. Math. 34 (2005), no. 3, 616-633.