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Mr James Tuite

Profile summary

Professional biography

I studied for my PhD in mathematics with the Open University under the supervision of Prof. Jozef Siran and Dr. Robert Brignall. My thesis title was 'Extremal Directed and Mixed Graphs'. In 2021 my research was supported by an LMS Early Career Fellowship. I am currently a Postdoctoral Fellow at the OU.

Research interests

My research is in extremal graph theory, particulary the degree/diameter and degree/girth problems. These problems concern the optimisation of the order of a network subject to restraints on the vertex degrees, diameter and girth; this theory has many applications, including the design of efficient communication systems and architectures for parallel computing. Many of my papers deal with the degree/geodecity problem, which generalises the degree/girth problem to the setting of directed and partially directed networks.

I also collaborate with researchers at the Renyi Institute in Budapest on Turan problems and related questions for directed graph,s and with researchers from the University of Kerala on the general position problem for graphs. I have wide interests in graph theory, including rainbow colourings, visibility problems, graph labelling and positional games.

Teaching interests

I currently tutor two Open University modules: M820 (Calculus of Variations and Advanced Calculus) and M823 (Analytic Number Theory).


On diregular digraphs with degree two and excess three (2019-08-15)
Tuite, James
Discrete Applied Mathematics, 266 (pp. 331-339)

Digraphs with degree two and excess two are diregular (2019-05)
Tuite, James
Discrete Mathematics, 342(5) (pp. 1233-1244)

On Total Regularity of Mixed Graphs with Order Close to the Moore Bound (2019)
Tuite, James and Erskine, Grahame
Graphs and Combinatorics, 35 (pp. 1253-1272)

Large Cayley graphs of small diameter (2018-12-11)
Erskine, Grahame and Tuite, James
Discrete Applied Mathematics, 250 (pp. 202-214)

On diregular digraphs with degree two and excess two (2018-03-31)
Tuite, James
Discrete Applied Mathematics, 238 (pp. 167-174)

New Bounds on k-Geodetic Digraphs and Mixed Graphs (2021)
Tuite, James and Erskine, Grahame
In : Extended Abstracts EuroComb 2021: European Conference on Combinatorics, Graph Theory and Applications (6-10 Sep, Barcelona (Online)) (pp. 778-783)