Tel: +27 82 821 4080 E-mail: [email protected] Position: Extraordinary Professor Academic qualifications: MSc (Australian National University) PhD (RAU) NRF rating: B2 Fields of interest: Graph Theory Research interests: Longest paths and cycles in graphs, vertex partition problems, local properties of graphs.

Publications over the past five years

Frick, M, A survey of the Path Partition Conjecture, Discussiones Math. Graph Theory 33 (2013), 117-131. 

 Van Aardt, SA, Burger, AP, Dunbar, JE, Frick, M, Harris, JM, Singleton, JE, An iterative approach to the Traceability Conjecture for Oriented Graphs, Electronic Journal of Combinatorics 20(1) (2013) #P59

Van Aardt, SA, Dunbar, JE, Frick, M, Nielsen, MH, Oellermann, O, Characterizations of k-traceable graphs and oriented graphs, Utilitas Math. 90, 2013.

Van Aardt, SA, Frick, M, Singleton, JE, Independent detour transversals in 3-deficient digraphs, Discussiones Math. Graph Theory 33 (2013) 261-275.

Van Aardt, SA, Burger, AP, Frick, M, An infinite family of planar hypohamiltonian oriented graphs, Graphs and Combinatorics 29 (2013) 729–733

Van Aardt, SA, Burger, AP, Frick, M, Llano, B, Zuazua, R, Infinite families of 2-hypohamiltonian/2-hypotraceable oriented graphs, Graphs and Combinatorics (2014) 30 783–800

Van Aardt, SA, Burger, AP, Frick, M, Llano, B, Thomassen , C, Zuazua, R, Destroying longest cycles in graphs and digraphs Discrete Applied Mathematics 186 (2015) 251–259

Van Aardt, SA, Burger, AP, Frick, M, Kemnitz, A, Schiermeyer, I, Hypohamiltonian oriented graphs of all possible orders, Graphs and Combinatorics 31 (2015) 1821–1831 (DOI 10.1007/s00373-015-1561-2)

Van Aardt, SA, Dunbar, JE, Frick, M, Lichiardopol, N, A linear bound towards the Traceability Conjecture, Electronic Journal of Combinatorics 22(4) (2015) no. P4.26

Frick, M, Llano, B, Zuazua, R, Self-diclique circulant digraphs, Mathematica Bohemica 140(3), 361–367 (2015)

Van Aardt, SA, Frick, M, Oellermann, O, de Wet J, Global cycle properties of locally connected, locally traceable and locally hamiltonian graphs, Discrete Applied Mathematics 205 (2016) 171–179.

Van Aardt, SA, Burger, AP, Frick, M, The Existence of Planar Hypotraceable Oriented Graphs, Discrete Mathematics & Theoretical Computer Science, March 16 #4, 2017.

Van Aardt, SA, Burger, AP, Brause, C, Frick,M, Kemnitz, A, Schiermeyer, I, Proper connection and size of graphs, Discrete Mathematics (http://dx.doi.org/10.1016/j.disc.2016.09.021).

De Wet JP, Frick M, Van Aardt SA  Hamiltonicity of Locally Hamiltonian and Locally Traceable Graphs. Discrete Applied Mathematics 236(2018) 137-152

Van Aardt SA, Burger AP, Frick M, Thomassen C, De Wet JP Hamilton cycles in sparse locally connected graphs. Discrete Applied Mathematics 257(2019) 276-288

De Wet JP, Frick M The Hamilton cycle problem for locally traceable and locally hamiltonian graphs. Discrete Applied Mathematics 266 (2019) 291-308

de Wet JP, Frick M, Nested locally Hamiltonian Graphs and the Oberly-Sumner Conjecture. Discuss. Math. Graph Theory 42 (2022) 1281-1312

Burger AP, De Wet JP, Frick M, Van Cleemput N, Zamfirescu CT Planar hypohamiltonian oriented graphs. To appear in Journal of Graph Theory 

Book Chapters

Frick M, Dunbar JE The Path Partition Conjecture, in Graph Theory: Favorite Conjectures and Open Problems, R. Gera, T.W. Haynes, S.T. Hedetniemi (eds), pp. 101-113, Springer Nature AG, Switzerland 2018.