Books

• Surveys in Combinatorics 2007, (joint editor with Anthony Hilton) Vol 346 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 2007.
  
  
• Complexity and cryptography - an introduction, (with Dominic Welsh), Cambridge University Press, Cambridge, 2006.
  
  

Papers

Submitted

• A solution to the 2/3 conjecture (with Rahil Baber).

  Published

• New Turan densities for 3-graphs (with Rahil Baber) The Electronic Journal of Combinatorics, 19 (2) 2012, #P22, 21 pages
  
  ExactDensityBounder.cpp C++ code to prove exact Turan densities for 3-graphs.
  
  DensityChecker.cpp C++ code to check proofs of exact Turan densities of 3-graphs.
  
  Installation and usage instructions for both programs can be found in the source files.
  
  Proof files from paper
  
  
• Vertex Ramsey Problems in the Hypercube (with John Goldwasser), SIAM J. Discrete Math. 26-2 (2012), pp. 838-853 ( Journal version)
  
  
• Hypergraphs do jump (with Rahil Baber), Combinatorics, Probability and Computing 20 161--171, 2011 (Journal version)
  C++ code and PSD matrices used in the proof: SolnFiles.zip
  
  
• The minimal density of triangles in tripartite graphs (with Rahil Baber and J. Robert Johnson), LMS Journal of Computation and Mathematics 13 388--413, 2010. (Journal version)
  
  C++ code to find all candidate extremal examples GraphFinder.cc
  
  
• Vertex Turan problems in the hypercube (with J. Robert Johnson), J. Combin. Theory Ser. A, (Journal version)
  
  
• On the density of 2-colorable 3-graphs in which any four points span at most two edges (with Klas Markstrom), J. Combin. Designs, 2009. (Journal version)
  
  
• G-intersection theorems for matchings and other graphs, (with J. Robert Johnson), Combin. Probab. Comput., 17(4):559--575, 2008. (Journal version)
  
  
• Extremal problems for t-partite and t-colorable hypergraphs, (with Dhruv Mubayi), Electron. J. Combin., 15(1), Research Paper 26, 9pp., 2008.
  
  
• Bloom maps, (with David Talbot), ANALCO08 (Workshop on Analytic Algorithms and Combinatorics), San Francisco, January 2008. (Journal version)
  
  
• Chromatic Turan problems and a new upper bound for the Turan density of K_4 ^-, European J. Combin., 28(8):2125--2142, 2007. (Journal version)
  
  
• A note on the jumping constant conjecture of Erdos, (with Peter Frankl, Yuejian Peng and Vojtech Rodl), J. Combin. Theory Ser. B, 97(2):204--216, 2007.
  
  
• The intersection structure of t-intersecting families, Electron. J. Combin., 12,Note 18, 4 pp., 2005.
  
  
• Graphs with the Erdos-Ko-Rado property, (with Fred Holroyd), Discrete Math., 293(1-3):165--176, 2005. (Journal version)
  
  
• Compression and Erdos-Ko-Rado graphs, (with Fred Holroyd and Claire Spencer), Discrete Math., 293 (1-3):155--164, 2005. (Journal version)
  
  
• A new Bollobas-type inequality and applications to intersecting families of sets", Discrete Math., 285(1-3):349--353, 2004.
  
  
• Counting consistent phylogenetic trees is #P-complete, (with Magnus Bordewich and Charles Semple), Adv. in Appl. Math., 33(2):416--430, 2004.
  
  
• The number of k-intersections of an intersecting family of r-sets, J. Combin. Theory Ser. A, 106(2):277--286, 2004. (Journal version)
  
  
• Intersecting families of separated sets, J. London Math. Soc. (2), 68(1):37--51, 2003. (Journal version)
  
  
• Lagrangians of hypergraphs, Combin. Probab. Comput., 11(2):199--216, 2002.