Nearly Hamilton cycles in sublinear expanders and applications
Abstract
Abstract We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in general graphs. These methods are of independent interest due to their potential for various applications to embedding problems in sparse graphs. In particular, using these tools, we make substantial progress towards a 20‐year‐old conjecture of Verstraëte, which asserts that for any given graph , nearly all vertices of every ‐regular graph can be covered by vertex‐disjoint ‐subdivisions. This significantly extends previous work on the conjecture by Kelmans, Mubayi and Sudakov, Alon and Kühn and Osthus. Additionally, we present applications of our methods to two other problems.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Commutative Algebra and Its Applications
Advanced Graph Theory Research
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Volume
- 113
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN