Projects per year
Abstract
A conjecture of Jackson from 1981 states that every d-regular oriented graph on n vertices with n≤4d+1 is Hamiltonian. We prove this conjecture for sufficiently large n. In fact we prove a more general result that for all α>0, there exists n0=n0(α) such that every d-regular digraph on n≥n0 vertices with d≥αn can be covered by at most n/(d+1) vertex-disjoint cycles, and moreover that if G is an oriented graph, then at most n/(2d+1) cycles suffice.
Original language | English |
---|---|
Journal | Forum of Mathematics, Sigma |
Publication status | Accepted/In press - 21 Dec 2024 |
Bibliographical note
Not yet published as of 10/02/2025Fingerprint
Dive into the research topics of 'Cycle Partitions in Dense Regular Digraphs and Oriented Graphs'. Together they form a unique fingerprint.Projects
- 2 Finished
-
Ramsey theory: an extremal perspective
Treglown, A. (Co-Investigator) & Lo, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/01/22 → 31/12/24
Project: Research Councils
-
Matchings and tilings in graphs
Lo, A. (Co-Investigator) & Treglown, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/03/21 → 29/02/24
Project: Research Councils
Activities
- 1 Guest lecture or Invited talk
-
Cycle Partition of Dense Regular Digraphs and Oriented Graphs
Lo, A. (Advisor)
21 Jun 2024Activity: Academic and Industrial events › Guest lecture or Invited talk