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Dirac-Type Questions For Hypergraphs — A Survey (Or More Problems For Endre To Solve)

2010; Springer Nature; Linguagem: Inglês

10.1007/978-3-642-14444-8_16

1217-4696

Vojtěch Rödl, Andrzej Ruciński,

Advanced Graph Theory Research

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.