Professor Robert Aldred

Research Interests

Prof Aldred's current research interests involve paths, cycles, matchings and colourings in graphs. Recently he has worked on bounding the number of cycles in a 3-connected cubic graph, determining the smallest 3-connected cubic planar non-Hamiltonian graphs of cyclic connectivity 4 and 5, factoring (colouring) regular graphs into linear forests of minimum length and classes of graphs which admit 1-factors with prescribed and proscribed edges.

Project/Thesis Possibilities

Prof Aldred is happy to supervise candidates in fourth year honours, M.A., M.Sc. and Ph.D research in Graph Theory, and would welcome enquiries from students wishing to consider problems in the areas mentioned above, and related areas, for possible research topics. He is also willing to act as a co-supervisor to any students whose main area of research may benefit from treatments involving combinatorial techniques. Such areas may, of course, arise from studying problems in disciplines outside of mathematics.

Some recent papers

• Aldred, R. E. L., and Thomassen, C., On the number of cycles in 3-connected cubic graphs.
• Aldred, R. E. L., and Wormald, N. C., More on the Linear k-arboricity of Regular Graphs, in Australasian Journal of Combinatorics, 18, p97 - 104, 1998
• Aldred, R. E. L., Bau, S., Holton, D. A., and McKay, B., Cycles through 23 vertices in 3-connected cubic planar graphs
• Aldred, R. E. L., and Plummer, M. D., On Matching Extensions with Prescribed and Proscribed Edge Sets II
• Aldred, R. E. L., Plummer, M. D., & Ruksasakchai, W. (2021). Asymmetric distance matching extension in 5-connected even planar triangulations. Australasian Journal of Combinatorics, 79(1), 1-14.
• Alahmadi, A., Aldred, R. E. L., & Thomassen, C. (2020). Cycles in 5-connected triangulations. Journal of Combinatorial Theory, Series B, 140, 27-44. doi: 10.1016/j.jctb.2019.04.005
• Aldred, R. E. L., Fujisawa, J., & Saito, A. (2020). Distance matching extension and local structure of graphs. Journal of Graph Theory, 93, 5-20. doi: 10.1002/jgt.22465
• Aldred, R. E. L., Plummer, M. D., & Ruksasakchai, W. (2020). Restricted matching in plane triangulations and near triangulations. Discrete Applied Mathematics, 284, 251-261. doi: 10.1016/j.dam.2020.03.037
• Aldred, R. E. L., Plummer, M. D., & Ruksasakchai, W. (2020). Distance restricted matching extension missing vertices and edges in 5-connected triangulations of the plane. Journal of Graph Theory, 95, 240-255. doi: 10.1002/jgt.22560