Work

Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree

Year: 2026

Type: article

Abstract: In 1960, Ghouila-Houri proved that every strongly connected directed graph G on n vertices with minimum degree at least n contains a directed Hamilton cycle. We asymptotically generalize this result by proving the following: every directed graph G on n vertices with minimum degree at least ( 1 + o ( 1 ) ) n contains every orientation of a Hamilton cycle, except for the directed Hamilton cycle in the case when G is not strongly connected. In fact, this minimum degree condition forces every orientation of a cycle in G of every possible length, other than perhaps the directed cycles.

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2026.10.004

Authors: Louis DeBiasio, Andrew Treglown

Institutions: Miami University, University of Birmingham

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funders: National Science Foundation, Engineering and Physical Sciences Research Council