He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős.
He was a student of Dénes Kőnig and an advisor of László Lovász.
The Edmonds–Gallai decomposition theorem, which was proved independently by Gallai and Jack Edmonds, describes finite graphs from the point of view of matchings.
[1] Gallai was the first to prove the higher-dimensional version of van der Waerden's theorem.
You can help Wikipedia by expanding it.This article about a European mathematician is a stub.