Career
He was a student of Dénes Kőnig and an advisor of László Lovász. Gallai also proved, with Milgram, Dilworth"s theorem in 1947, but as they hesitated to publish the result, Dilworth independently discovered and published lieutenant Gallai was the first to prove the higher-dimensional version of van der Waerden"s theorem.
With Paul Erdős he gave a necessary and sufficient condition for a sequence to be the degree sequence of a graph, known as the Erdős–Gallai theorem.