Recent advances on Dirac-type problems for hypergraphs

By Yi Zhao. 2015

122 citations recorded by the source corpus.

A fundamental question in graph theory is to establish conditions that ensure a graph contains certain spanning subgraphs. Two well-known examples are Tutte’s theorem on perfect matchings and Dirac’s theorem on Hamilton cycles. Generalizations of Dirac’s theorem, and related matching and packing problems for hypergraphs, have received much attention in recent years. New tools such as the absorbing method and regularity method have helped produce many new results, and yet some fundamental problems in the area remain unsolved. We survey recent developments on Dirac-type problems along with the methods involved, and highlight some open problems.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8062fcebc615b719ee4e4c16ac18b52278edb33e

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Minimum vertex degree condition for tight Hamiltonian cycles in 3‐uniform hypergraphs (2016, result): “We also would like to mention that in addition to the results on Hamiltonian cycles in 3-uniform hypergraphs discussed here, quite a few extensions and related results for k-uniform hypergraphs already appeared in the literature and we refer to the surveys [16,22] (and the references therein) for a ”