Open Research Online

Donovan, Diane. M.; Grannell, Mike J. and Yazici, Emine. Sule (2024). On maximal partial Latin hypercubes. Designs, Codes and Cryptography, 92(2) pp. 419–433.

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Grannell, Mike J.; Griggs, Terry S.; Lo Faro, Giovanni and Tripodi, Antoinette (2022). Avoidance in bowtie systems. Ars Mathematica Contemporanea, 22(3), article no. #P3.07.

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Demirkale, Fatih; Donovan, Diane and Grannell, Mike (2021). Anti-Pasch optimal coverings with triples. Journal of Combinatorial Designs, 29(2) pp. 84–113.

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Donovan, Diane; Grannell, Mike and Yazici, Emine Şule (2020). Embedding partial Latin squares in Latin squares with many mutually orthogonal mates. Discrete Mathematics, 343(6), article no. 111835.

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Demirkale, Fatih; Donovan, Diane and Grannell, Mike (2020). Maximum partial triple systems on 16 and 17 points. Utilitas Mathematica, 114 pp. 255–276.

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Donovan, Diane M.; Grannell, Mike and Yazıcı, Emine Ş. (2020). Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results. Commentationes Mathematicae Universitatis Carolinae, 61(4) pp. 437–457.

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Demirkale, Fatih; Donovan, Diane and Grannell, Mike (2019). Anti-Pasch optimal packings with triples. Journal of Combinatorial Designs, 27(6) pp. 353–368.

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Donovan, Diane M. and Grannell, Mike J. (2018). On the number of transversals in a class of Latin squares. Discrete Applied Mathematics, 235 pp. 202–205.

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Donovan, Diane and Grannell, Mike (2018). On the number of additive permutations and Skolem-type sequences. Ars Mathematica Contemporanea, 14 pp. 415–432.

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Grannell, Mike and Knor, Martin (2016). Pasch trades on the projective triple system of order 31. Journal of Combinatorial Mathematics and Combinatorial Computing, 96 pp. 23–32.

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Grannell, M. J. and Lovegrove, G. J. (2016). Identical twin Steiner triple systems. The Australasian Journal of Combinatorics, 66(1) pp. 130–141.

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Grannell, Mike and Schroeder, Justin (2015). Biembeddings of 2-rotational Steiner triple systems. Electronic Journal of Combinatorics, 22(2), article no. P2.23.

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Grannell, M. J. and Knor, M. (2014). Rigid Steiner triple systems obtained from projective triple systems. Journal of Combinatorial Designs, 22(7) pp. 279–290.

Grannell, Mike and McCourt, Thomas (2014). Doubly even orientable closed 2-cell embeddings of the complete graph. Electronic Journal of Combinatorics, 21(1), article no. P1.22.

Grannell, Mike J.; Griggs, Terry S.; Máčajová, Edita and Škoviera, Martin (2013). Coloring cubic graphs by point-intransitive Steiner triple systems. Journal of Graph Theory, 74(2) pp. 163–181.

Donovan, D. M. and Grannell, M. J. (2013). On the number of transversal designs. Journal of Combinatorial Theory, Series A, 120(7) pp. 1562–1574.

Grannell, Mike and Lovegrove, Graham (2013). Maximizing the number of Pasch configurations in a Steiner triple system. Bulletin of the Institute of Combinatorics and its Applications, 69 pp. 23–35.

Grannell, M. J.; Griggs, T. S.; Lo Faro, G. and Tripodi, A. (2013). Configurations in bowtie systems. Aequationes Mathematicae, 85(3) pp. 347–358.

Grannell, M. J. and Knor, M. (2013). Dihedral biembeddings and triangulations by complete and complete tripartite graphs. Graphs and Combinatorics, 29(4) pp. 921–932.

Grannell, M. J.; Griggs, T. S. and Lovegrove, G. J. (2013). Even-cycle systems with prescribed automorphism groups. Journal of Combinatorial Designs, 21(4) pp. 142–156.

Grannell, M. J. and Knor, M. (2012). On the number of triangular embeddings of complete graphs and complete tripartite graphs. Journal of Graph Theory, 69(4) pp. 370–382.

Grannell, M. J. and Knor, M. (2012). Biembedding Abelian groups with mates having transversals. Journal of Combinatorial Designs, 20(2) pp. 81–88.

Donovan, D. M. and Grannell, M. J. (2012). On the number of designs with affine parameters. Designs, Codes and Cryptography, 63(1) pp. 15–27.

Grannell, Mike and Knor, Martin (2012). Biembeddings of metacyclic groups and triangulations of orientable surfaces by complete graphs. Electronic Journal of Combinatorics, 19(3) P29.

Grannell, Mike and Knor, Martin (2011). A construction for biembeddings of Latin squares. Electronic Journal of Combinatorics, 18(1)

Donovan, Diane M.; Grannell, Mike J.; Griggs, Terry S.; Lefevre, James G. and McCourt, Thomas (2011). Self-embeddings of cyclic and projective Steiner quasigroups. Journal of Combinatorial Designs, 19(1) pp. 16–27.

Donovan, D. M. and Grannell, M. J. (2011). Designs having the parameters of projective and affine spaces. Designs, Codes and Cryptography, 60(3) pp. 225–240.

Drizen, A.L.; Grannell, Mike and Griggs, Terry (2011). Pasch trades with a negative block. Discrete Mathematics, 311(21) pp. 2411–2416.

Grannell, Mike and Knor, Martin (2011). Biembeddings of Latin squares obtained from a voltage construction. Australasian Journal of Combinatorics, 51 pp. 259–270.

Donovan, D. M.; Drápal, A.; Grannell, M. J.; Griggs, T. S. and Lefevre, J. G. (2010). Quarter-regular biembeddings of Latin squares. Discrete Mathematics, 310(4) pp. 692–699.

Grannell, M. J. and Knor, M. (2010). Biembeddings of Abelian groups. Journal of Combinatorial Designs, 18(1) pp. 71–83.

Chicot, K. M.; Grannell, M. J.; Griggs, T. S. and Webb, B. S. (2010). On sparse countably infinite Steiner triple systems. Journal of Combinatorial Designs, 18(2) pp. 115–122.

Grannell, M. J. and Knor, M. (2010). A lower bound for the number of orientable triangular embeddings of some complete graphs. Journal of Combinatorial Theory, Series B, 100(2) pp. 216–225.

Colbourn, Charles J.; Forbes, Anthony D.; Grannell, Mike J.; Griggs, Terry S.; Kaski, Petteri; Östergard, Patric R. J.; Pike, David A. and Pottonen, Olli (2010). Properties of the Steiner Triple Systems of Order 19. Electronic Journal of Combinatorics, 17(1) article no. R98.

Grannell, M. J. and Knor, M. (2010). An enumeration of minimum genus orientable embeddings of some complete bipartite graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, 73, pp. 95–102.

Grannell, M. J. (2010). Some rigid Steiner 5-designs. Journal of Combinatorial Designs, 18(5) pp. 392–400.

Donovan, D. M.; Grannell, M. J. and Griggs, T. S. (2010). Third-regular bi-embeddings of Latin squares. Glasgow Mathematical Journal, 52(3) pp. 497–503.

Donovan, D. M.; Grannell, M. J.; Griggs, T. S. and Lefevre, J. G. (2010). On parity vectors of Latin squares. Graphs and Combinatorics, 26(5) pp. 673–684.

Grannell, M.J. and Korzhik, V.P. (2009). Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs. Discrete Mathematics, 309(9) pp. 2847–2860.

Lefevre, J. G.; Donovan, D. M.; Grannell, M. J. and Griggs, T. S. (2009). A constraint on the biembedding of Latin squares. European Journal of Combinatorics, 30(2) pp. 380–386.

Grannell, M. J.; Griggs, T. S. and Knor, M. (2009). On biembeddings of Latin squares. Electronic Journal of Combinatorics, 16(1) R106.

Forbes, A. D.; Grannell, M. J. and Griggs, T. S. (2009). Further 6-sparse Steiner Triple Systems. Graphs and Combinatorics, 25(1) pp. 49–64.

Grannell, M. J.; Griggs, T. S. and Stanton, R. G. (2009). Bounds on g(1)((5)) (v) for v equivalent to 9, 13, 17 (mod 20). Utilitas Mathematica, 78 pp. 79–92.

Grannell, M. J.; Griggs, T. S.; LoFaro, G. and Tripodi, A. (2009). Small bowtie systems: an enumeration. Journal of Combinatorial Mathematics and Combinatorial Computing, 70 pp. 149–159.

Grannell, Mike J.; Griggs, Terry S.; Máčajová, Edita and Škoviera, Martin (2009). Wilson-Schreiber colourings of cubic graphs. Electronic Notes in Discrete Mathematics, 34 pp. 225–229.

Grannell, M. J.; Griggs, T. S. and Quinn, K. A. S. (2009). Smallest defining sets of directed triple systems. Discrete Mathematics, 309(14) pp. 4810–4818.

Grannell, M. J.; Griggs, T. S. and Knor, M. (2009). Orientable biembeddings of Steiner triple systems of order 15. Journal of Combinatorial Mathematics and Combinatorial Computing, 68 pp. 129–136.

Grannell, Mike and Griggs, Terry (2009). Embeddings and designs. In: Wilson, Robin and Beineke, LW eds. Topics in Topological Graph Theory. Cambridge: Cambridge University Press, pp. 268–288.

Grannell, M. J.; Griggs, T. S.; Knor, M. and Thrower, A. R. W. (2008). A census of the orientable biembeddings of Steiner triple systems of order 15. Australasian Journal of Combinatorics, 42, pp. 253–259.

Grannell, M. J.; Griggs, T. S. and Knor, M. (2008). Biembeddings of symmetric configurations and 3-homogeneous Latin trades. Commentationes Mathematicae Universitatis Carolinae, 49(3) pp. 411–420.

Grannell, M. J. and Griggs, T. S. (2008). A lower bound for the number of triangular embeddings of some complete graphs and complete regular tripartite graphs. Journal of Combinatorial Theory, Series B, 98 pp. 637–650.

Forbes, A. D.; Grannell, M. J. and Griggs, T. S. (2007). New type B colorable S(2, 4, v) designs. Journal of Combinatorial Designs, 15(4) pp. 357–368.

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2007). On 6-sparse Steiner triple systems. Journal of Combinatorial Theory, Series A, 114(2) pp. 235–252.

Grannell, Mike J.; Griggs, Terry S. and Siran, Jozef (2007). Hamiltonian embeddings from triangulations. Bulletin of the London Mathematical Society, 39(3) pp. 447–452.

Forbes, Anthony; Grannell, Mike and Griggs, Terry (2007). Distance and fractional isomorphism in Steiner triple systems. Rendiconti del Circolo Matematico di Palermo Serie II, 56, pp. 17–32.

Grannell, Mike and Griggs, Terry (2007). Designs and topology. In: Hilton, A. and Talbot, J. eds. Surveys in Combinatorics 2007. London Mathematical Society Lecture Note Series 346, London Mat (346). Cambridge, UK: Cambridge University Press, pp. 121–174.

Forbes, Anthony; Grannell, Mike; Griggs, Terry and Stanton, R. G. (2007). On the small covering numbers $g^{(5)}_1(v)$ . Utilitas Mathematica, 74, pp. 77–96.

Forbes, Anthony; Grannell, Mike and Griggs, Terry (2007). The design of the century. Mathematica Slovaca, 57(5) pp. 495–499.

Grannell, Mike; Griggs, Terry and Knor, M. (2007). Biembeddings of Latin squares of side 8. Quasigroups and Related Systems, 15(2) pp. 273–278.

Bennett, G. K.; Grannell, M. J.; Griggs, T. S. and Siran, J. (2006). Small surface trades in triangular embeddings. Discrete Mathematics, 306(21) pp. 2637–2646.

Grannell, Mike J.; Griggs, Terry S. and Street, Anne Penfold (2006). A flaw in the use of minimal defining sets for secret sharing schemes. Designs, Codes and Cryptography, 40(2) pp. 225–236.

Grannell, M. J.; Griggs, T. S.; Knor, M. and Siran, J. (2006). Triangulations of orientable surfaces by complete tripartite graphs. Discrete Mathematics, 306(6) pp. 600–606.

Bennett, G.K.; Grannell, M.J. and Griggs, T.S. (2006). Orientable self-embeddings of Steiner triple systems of order 15. Acta Mathematica Universitatis Comenianae, 75(2) pp. 163–172.

Adams, P.; Bryant, D.; Grannell, Mike and Griggs, Terry (2006). Diagonally switchable 4-cycle systems. Australasian Journal of Combinatorics, 34, pp. 145–152.

Grannell, Mike J.; Griggs, Terry S. and Siran, Jozef (2005). Maximum genus embeddings of Steiner triple systems. European Journal of Combinatorics, 26(3-4) pp. 401–416.

Forbes, A. D.; Grannell, M. J. and Griggs, T. S. (2005). Steiner triple systems and existentially closed graphs. Electronic Journal of Combinatorics, 12(1)

Bryant, D. E.; Grannell, Mike and Griggs, Terry (2005). Large sets of cycle systems on nine points. Journal of Combinatorial Mathematics and Combinatorial Computing, 53, pp. 95–102.

Forbes, Anthony; Grannell, Mike and Griggs, Terry (2005). On independent sets. Mathematica Slovaca, 55(4) pp. 375–377.

Grannell, Mike; Griggs, Terry; Stanton, R. G. and Whitehead, C. A. (2005). On the covering number $g_1^{(4)}(18)$ . Utilitas Mathematica, 68, pp. 131–143.

Grannell, M.J.; Griggs, T.S and Knor, M. (2004). Biembeddings of Latin squares and Hamiltonian decompositions. Glasgow Mathematical Journal, 46(3) pp. 443–457.

Bennett, G. K.; Grannell, Mike and Griggs, Terry (2004). Exponential lower bounds for the numbers of Skolem-type sequences. Ars Combinatoria, 73 pp. 101–106.

Grannell, M.J. and Korzhik, V.P. (2004). Nonorientable biembeddings of Steiner triple systems. Discrete Mathematics, 285(1-3) pp. 121–126.

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2004). Independent sets in Steiner triple systems. Ars Combinatoria, 72 pp. 161–169.

Bryant, Darryn; Grannell, Mike; Griggs, Terry and Macaj, Martin (2004). Configurations in 4-cycle systems. Graphs and Combinatorics, 20(2) pp. 161–179.

Grannell, Mike; Griggs, Terry; Knor, Martin and Skoviera, Martin (2004). A Steiner triple system which colours all cubic graphs. Journal of Graph Theory, 46(1) pp. 15–24.

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2004). Configurations and trades in Steiner triple systems. Australasian Journal of Combinatorics, 29 pp. 75–84.

Grannell, Mike; Griggs, Terry and Santon, R. G. (2004). Minimal perfect bicoverings of K_v with block sizes two, three and four. Ars Combinatoria, 71 pp. 125–138.

Bennett, G. K.; Grannell, M. J. and Griggs, T. S. (2004). Non-orientable biembeddings of Steiner triple systems of order 15. Acta Mathematica Universitatis Comenianae, 73(1) pp. 101–106.

Grannell, Mike; Griggs, Terry and Stanton, R. G. (2004). On $\lambda$ -fold coverings with maximum block size four for $\lambda = 3, 4$ and 5. Journal of Combinatorial Mathematics and Combinatorial Computing, 51, pp. 137–158.

Grannell, M. J.; Griggs, T. S. and Stanton, RG (2004). On $\lambda$ -fold coverings with maximum block size four for $\lambda\ge 6$ . Utilitas Mathematica, 66, pp. 221–230.

Grannell, M. J.; Griggs, T. S. and Knor, M. (2004). Biembeddings of symmetric configurations of triples. In: Proceedings of the MaGiA Conference, 15-17 Oct 2004, Kocovce.

Grannell, M.J.; Griggs, T.S.; Korzhik, V.P. and Siran, Jozef (2003). On the minimal nonzero distance between triangular embeddings of a complete graph. Discrete Mathematics, 269(1-3) pp. 149–160.

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2003). On colourings of Steiner triple systems. Discrete Mathematics, 261(1-3) pp. 255–276.

Bryant, Darryn; Grannell, Mike; Griggs, Terry and Maenhaut, Barbara (2003). On the volume of 4-cycle trades. Graphs and Combinatorics, 19(1) pp. 53–63.

Bryant, D.; Grannell, M. J. and Griggs, T. S. (2003). Large sets of large sets of Steiner triple systems of order 9. Utilitas Mathematica, 64, pp. 115–118.

Grannell, M. J.; Griggs, T. S.; Maenhaut, B. M.; Quinn, K. A. S. and Stanton, R. G. (2003). More on exact bicoverings of 12 points. Ars Combinatoria, 69 pp. 197–213.

Grannell, Mike; Griggs, Terry and Knor, M. (2003). Face two-colourable triangulations of $K_{13}$ . Journal of Combinatorial Mathematics and Combinatorial Computing, 47, pp. 75–81.

Grannell, M. J.; Griggs, T. S. and Knor, M. (2003). Regular Hamiltonian embeddings of the complete bipartite graph $K_{n,n}$ in an orientable surface. Congressus Numerantium, 163, pp. 197–205.

Bennett, G.K.; Grannell, M.J. and Griggs, T.S. (2002). On the bi-embeddability of certain Steiner triple systems of order 15. European Journal of Combinatorics, 23(5) pp. 499–505.

Franek, F.; Grannell, M.J.; Griggs, T.S. and Rosa, A. (2002). On large sets of v-1 L-intersecting Steiner triple systems of order v. Designs, Codes and Cryptography, 26(1-3) pp. 243–256.

Bennett, G.K.; Grannell, M.J. and Griggs, T.S. (2002). Cyclic bi-embeddings of Steiner triple systems on 12s+7 points. Journal of Combinatorial Designs, 10(2) pp. 92–110.

Grannell, M. J.; Griggs, T. S. and Siran, J. (2002). Recursive constructions for triangulations. Journal of Graph Theory, 39(2) pp. 87–107.

Grannell, M.J.; Griggs, T.S. and Holroyd, F.C. (2001). Modular gracious labellings of trees. Discrete Mathematics, 231(1-3) pp. 199–219.

Grannell, M.J.; Griggs, T.S and Hill, R. (2001). The Triangle chromatic index of Steiner triple systems. Australasian Journal of Combinatorics, 23 pp. 217–230.

Bennett, G. K.; Grannell, M. J. and Griggs, T. S. (2001). Cyclic bi-embeddings of Steiner triple systems on 31 points. Glasgow Mathematical Journal, 43(1) pp. 145–151.

Bennett, G. K.; Grannell, M. J. and Griggs, T. S. (2001). Bi-embeddings of Steiner triple systems of order 15. Graphs and Combinatorics, 17(2) pp. 193–197.

Allston, J. L.; Grannell, M. J.; Griggs, T. S.; Quinn, K. A. S. and Stanton, R. G. (2000). On exact bicoverings of 12 points. Ars Combinatoria, 55 pp. 147–159.

Ling, A. C. H.; Colbourn, C. J.; Grannell, M. J. and Griggs, T. S. (2000). Construction techniques for anti-Pasch Steiner triple systems. Journal of the London Mathematical Society, 61(3) p. 641.

Grannell, M. J.; Griggs, T. S. and Whitehead, C. A. (2000). The resolution of the anti-Pasch conjecture. Journal of Combinatorial Designs, 8(4) pp. 300–309.

Grannell, M. J.; Griggs, T. S.; Quinn, K. A. S. and Stanton, R. G. (2000). Triple systems with tripoints. Utilitas Mathematica, 57, pp. 97–108.

Grannell, M. J.; Griggs, T. S.; Kocay, W. L.; Quinn, K. A. S. and Stanton, R. G. (2000). Proper edge-colourings of complete graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, 33, pp. 103–116.

Grannell, M. J.; Griggs, T. S.; Quinn, K. A. S. and Stanton, R. G. (2000). Non-isomorphic solutions for some triple systems with bipoints. Utilitas Mathematica, 57, pp. 97–108.

Grannell, M. J.; Griggs, T S. and Quinn, K. A. S. (2000). All admissible $3$ - $(v, 4, \lambda)$ directed designs exist. Journal of Combinatorial Mathematics and Combinatorial Computing, 35, pp. 65–70.

Grannell, Mike; Griggs, Terry and Holroyd, Fred (2000). Cuboctahedron designs. Journal of Combinatorial Mathematics and Combinatorial Computing, 35, pp. 185–191.

Allston, J. L.; Grannell, M. J.; Griggs, T. S. and Stanton, R. G. (2000). Pairwise balanced designs on $4s+1$ points with longest block of cardinality $2s$ . Utilitas Mathematica, 58, pp. 97–107.