Tibor Gallai (born Tibor Grünwald, 15 July 1912 to 2 January 1992) was a Hungarian mathematician who worked in combinatorics, especially 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, and a corresponding member of the Hungarian Academy of Sciences from 1991. The Edmonds-Gallai decomposition theorem, proved independently by Gallai and Jack Edmonds, describes finite graphs from the point of view of matchings. Gallai was the first to prove the higher-dimensional version of van der Waerden's theorem, and with Erdős he gave the Erdős-Gallai condition for a sequence to be the degree sequence of a graph.
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He worked in combinatorics, especially in graph theory, and was a lifelong friend and collaborator of Paul Erdős.
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Unaware of Melchior's proof, Paul Erdős (1943) again stated the conjecture, which was subsequently proved by Tibor Gallai, and soon afterwards by other authors.
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