He worked mainly in graph theory, and is known for introducing a graph-theoretic view of pursuit-evasion problems (Parsons 1976, 1978). He obtained his Ph.D. from Princeton University in 1966 under the supervision of Albert W. Tucker.
- Parsons, T. D. (1976). "Pursuit-evasion in a graph". Theory and Applications of Graphs. Springer-Verlag. pp. 426–441.
- Parsons, T.D. (1978). "The search number of a connected graph". Proc. 10th Southeastern Conf. Combinatorics, Graph Theory, and Computing. pp. 549–554.
Memorial articles in
- Journal of Graph Theory vol. 12
- Discrete Mathematics vol. 78
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