Publications

Preprints

  1. A.C. Burgess, P.H. Danziger and A. Lacaze-Masmonteil. A complete solution to the directed Oberwolfach problem of order 2 (mod 4) with cycles of even lengths. (Arxiv:2602.16888)
  2. A.C. Burgess, N.E. Clarke, S.L. Fitzpatrick and M.A. Huggan. Deduction with k moves. (Arxiv:2510.24959)
  3. A.C. Burgess, P. Danziger, D. Donovan, T. Kemp, J.G. Lefevre, D.A. Pike and E.Ş. Yazıcı. Colourings of group divisible designs and maximum packings. (Arxiv:2510.05375)
  4. A.C. Burgess, D. Dyer, K. Ojakian, L. Wang, M. Xiao and B. Yang. Deduction, constrained zero-forcing and constrained searching. (Arxiv:2410.22962)
  5. A. Burgess, F. Merola and T. Traetta. On circular external difference families. (Arxiv:2509.02731)

Papers accepted for publication in refereed journals

  1. A.C. Burgess, C.W. Jones and D.A. Pike. Extending graph burning to hypergraphs. Ars Mathematica Contemporanea, to appear. (Link to article)
  2. A.C. Burgess, J. Hawkin, A. Howse, C.W. Jones and D.A. Pike. Proportion-based hypergraph burning. Canadian Journal of Mathematics, to appear. (Preprint: Arxiv:2408.06283)

Papers published in refereed journals

  1. A.C. Burgess, P. Danziger, D. Horsley and M.T. Javed. Packing designs with large block size. Designs, Codes and Cryptography 94 (2026), Article #20. (Link to article)
  2. A.C. Burgess, J. Hawkin, A. Howse, J. Marcoux and D.A. Pike. Distance-restricted firefighting on finite graphs. Theoretical Computer Science 1061 (2026), Article #115658. (Link to article)
  3. A.C. Burgess, J. Marcoux and D.A. Pike. Firefighting with a distance-based restriction. Discrete Applied Mathematics 378 (2026), 480–491. (Link to article)
  4. A.C. Burgess, N.J. Cavenagh, P. Danziger and D.A. Pike. Weak colouring of Kirkman triple systems. Designs, Codes and Cryptography 93 (2025), 3159–3179. (Link to article)
  5. A.C. Burgess, D. Dyer and M. Farahani. An introduction to the deduction number. Discrete Applied Mathematics 369 (2025), 20–27. (Link to article)
  6. A.C. Burgess, R.D. Luther and D.A. Pike. Existential closure in uniform hypergraphs. Discrete Mathematics 348 (2025), Article #114372. (Link to article)
  7. A.C. Burgess, R.D. Luther and D.A. Pike. Existential closure in line graphs. Graphs and Combinatorics 40 (2024), Article #101. (Link to article)
  8. A. Burgess and F. Merola. On equitably 2-colourable odd cycle decompositions. Journal of Combinatorial Designs 32 (2024), 419–437. (Link to article)
  9. A.C. Burgess, R.D. Luther and D.A. Pike. The edge-connectivity of vertex-transitive hypergraphs. Journal of Graph Theory 105 (2024), 252–259. (Link to article)
  10. A.C. Burgess, P. Danziger, A. Pastine and T. Traetta. Constructing uniform 2-factorizations via row-sum matrices: Solutions to the Hamilton-Waterloo problem. Journal of Combinatorial Theory Series A 201 (2024), Article #105803. (Link to article)
  11. A.C. Burgess, N.J. Cavenagh and D.A. Pike. Mutually orthogonal cycle systems. Ars Mathematica Contemporanea 23 (2023), Article #P2.05. (Link to article)
  12. A.C. Burgess, P. Danziger and T. Traetta. On the Oberwolfach problem for single-flip 2-factors via graceful labelings. Journal of Combinatorial Theory Series A 189 (2022), Article #105611. (Link to article)
  13. K.D. Barnetson, A. Burgess, J. Enright, J. Howell, D.A. Pike and B. Ryan. The firebreak problem. Networks 77 (2021), 372–382. (Link to article)
  14. A.C. Burgess, P. Danziger and M.T. Javed. Cycle decompositions of complete digraphs. Electronic Journal of Combinatorics 28 (2021), Article #P1.35. (Link to article)
  15. A. Burgess and F. Merola. Equitably 2-colourable even cycle systems. Australasian Journal of Combinatorics 79 (2021), 435–453. (Link to article)
  16. A.C. Burgess, R.A. Cameron, N.E. Clarke, P. Danziger, S. Finbow, C.W. Jones and D.A. Pike. Cops that surround a robber. Discrete Applied Mathematics 285 (2020), 552–566. (Link to article)
  17. A. Burgess, F. Merola and T. Traetta. Cyclic cycle systems of the complete multipartite graph. Journal of Combinatorial Designs 28 (2020), 224–260. (Link to article)
  18. A.C. Burgess, P. Danziger and T. Traetta. The Hamilton-Waterloo Problem with even cycle lengths. Discrete Mathematics 342 (2019), 2213–2222. (Link to article)
  19. A.C. Burgess, P. Danziger and T. Traetta. On the generalized Oberwolfach Problem. Ars Mathematica Contemporanea 17 (2019), 67–78. (Link to article)
  20. N. Bolohan, I. Buchanan, A. Burgess, M. Šajna and R. Van Snick. On the spouse-loving variant of the Oberwolfach problem. Journal of Combinatorial Designs 27 (2019), 251–260. (Link to article)
  21. A. Burgess, N. Francetić and M.Šajna. On the directed Oberwolfach problem with equal cycle lengths: the odd case. Australasian Journal of Combinatorics 71 (2018), 272–292. (Link to article)
  22. A.C. Burgess, P. Danziger and T. Traetta. On the Hamilton-Waterloo Problem with cycle lengths of distinct parities. Discrete Mathematics 341 (2018), 1636 1644. (Link to article)
  23. A.C. Burgess, P. Danziger and T. Traetta. On the Hamilton-Waterloo Problem with odd cycle lengths. Journal of Combinatorial Designs 26 (2018), 51 83. (Link to article)
  24. A.C. Burgess, P. Danziger and T. Traetta. On the Hamilton-Waterloo Problem with odd orders. Journal of Combinatorial Designs 25 (2017), 258–287. (Link to article)
  25. S. Akbari, A.C. Burgess, P. Danziger and E. Mendelsohn. Zero-sum flows for triple systems. Discrete Mathematics 340 (2017), 416–425. (Link to article)
  26. R.J.R. Abel, R.F. Bailey, A.C. Burgess, P. Danziger and E. Mendelsohn. On generalized Howell designs with block size three. Designs, Codes and Cryptography 81 (2016), 365–391. (Link to article)
  27. D. Bryant, A. Burgess and P. Danziger. Decompositions of complete graphs into bipartite 2-regular subgraphs. Electronic Journal of Combinatorics 23 (2016), Article #P2.1. (Link to article)
  28. A. Burgess, P. Danziger, E. Mendelsohn and B. Stevens. Orthogonally resolvable cycle decompositions. Journal of Combinatorial Designs 23 (2015), 328–351. (Link to article)
  29. A. Burgess and M. Šajna. On the directed Oberwolfach Problem with equal cycle lengths. Electronic Journal of Combinatorics 21 (2014), Article #P1.15. (Link to article)
  30. A. Bonato and A. Burgess. Cops and robbers on graphs based on designs. Journal of Combinatorial Designs 21 (2013), 404–418. (Link to article)
  31. R.F. Bailey and A.C. Burgess. Generalized packing designs. 313 (2013), 1167–1190. (Link to article)
  32. R.F. Bailey, A.C. Burgess, M.S. Cavers and K. Meagher. Generalized covering designs and clique coverings. Journal of Combinatorial Designs 19 (2011), 378–406. (Link to article)
  33. A. Burgess and M. Šajna. Closed trail decompositions of complete equipartite graphs. Journal of Combinatorial Designs 17 (2009), 374–403. (Link to article)
  34. A.C. Burgess and D.A. Pike. Colouring even cycle systems. Discrete Mathematics 308 (2008), 962–973. (Link to article)
  35. A.C. Burgess and D.A. Pike. Coloring 4-cycle systems. Journal of Combinatorial Designs 14 (2006), 56–65. (Link to article)

Papers published in refereed conference proceedings

  1. A.C. Burgess, P.H. Danziger and T. Traetta. A survey on constructive methods for the Oberwolfach Problem and its variants. New Advances in Designs, Codes and Cryptography (Stinson66, Toronto, Canada, June 13–17, 2022). Eds: C.J. Colbourn and J.H. Dinitz. Fields Institute Communications, Volume 86. Springer Cham, 2024. (Link to article)