 Tutte completed a doctorate in mathematics from Cambridge in 1948 under the supervision of Shaun Wylie, who had also worked at Bletchley Park on Tunny.In late 1945, Tutte resumed his studies at Cambridge, now as a graduate student in mathematics.He published some work begun earlier, one a now famous paper that characterises which graphs have a perfect matching, and another that constructs a non-Hamiltonian graph.