Hamilton cycles in graphs and hypergraphs: an extremal perspective

By D. Kühn, Deryk Osthus. 2014

92 citations recorded by the source corpus.

As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi-randomness. These concepts and other recent techniques have led to the solution of several long-standing problems in the area. New aspects have also emerged, such as resilience, robustness and the study of Hamilton cycles in hypergraphs. We survey these developments and highlight open problems, with an emphasis on extremal and probabilistic approaches.

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

View Paper: https://www.semanticscholar.org/paper/a3781a5406d16228cd35ed496ad0fafe8372fa60

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Peter Keevash
2. Deryk Osthus
3. D. Kühn
4. Allan Siu Lun Lo
5. Jie Han
6. Richard Mycroft
7. Yi Zhao

In Discrete Mathematics and Combinatorics

1. Peter Keevash
2. Deryk Osthus
3. D. Kühn
4. Allan Siu Lun Lo
5. Jie Han
6. Matthew Kwan
7. Yi Zhao
8. Stefan Glock

In Geometry and Topology

1. Peter Keevash
2. Allan Siu Lun Lo
3. Deryk Osthus
4. D. Kühn
5. Jie Han

Citations in the corpus

• The existence of designs (2014, background): “Absorption has recently been a powerful tool for many other problems; see the survey [28].”
• Proof of the 1-factorization and Hamilton Decomposition Conjectures (2014, background): “Further questions in the area are discussed in the recent survey [23].”