Dirac-type questions for hypergraphs a survey (Or more problems for endre to solve)

Abstract

Dedicated to Endre Szemerédi on the occasion of his 70th birthday In 1952 Dirac [8] proved a celebrated theorem stating that if the minimum degree δ(G) in an n-vertex graph G is at least n/2 then G contains a Hamiltonian cycle. In 1999, Katona and Kierstead initiated a new stream of research devoted to studying similar questions for hypergraphs, and subsequently, for perfect matchings. A pivotal role in achieving some of the most important results in both these areas was played by Endre Szemerédi. In this survey we present the current state-of-art and pose some open problems.