Current research interests:

Professor Thomas works in Graph Theory, a relatively young field that is becoming increasingly more important, because of applications in other areas of mathematics, physics, chemistry, engineering and social sciences. His work has concentrated on structural results and their use in the design of theoretically efficient and practical graph algorithms. Professor Thomas' results include:

• a new and simpler proof of the Four Color Theorem,
• a proof of Hadwiger's conjecture for K₆-free graphs,
• a proof of Sachs' linkless embedding conjecture,
• structure theory for excluding infinite graphs,
• proofs of conjectures of Plummer, Grunbaum, and Nash-Williams concerning Hamiltonian graphs on surfaces,
• a proof of Younger's conjecture about packing directed circuits,
• a solution to a 1913 question of Pólya, which also solves the "even directed circuit problem" and several other equivalent problems,
• a proof of the Strong Perfect Graph Conjecture of Berge from 1960.

Professor Thomas serves on the Editorial Boards of

• Journal of Graph Theory
• Graphs and Combinatorics
• Discrete Mathematics and Theoretical Computer Science
• SIAM Journal on Discrete Mathematics

and frequently lectures about his work.