Bounded diameter monochromatic component covers
Abstract
Abstract Ryser conjectured that every ‐edge‐coloured complete graph can be covered by monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger — that every ‐edge‐coloured complete graph can be covered by monochromatic trees of bounded diameter . Here we show that the two conjectures are equivalent. As immediate corollaries we obtain new results about Milićević's Conjecture, most notably that it is true for . We also obtain several new cases of a generalization of Milićević's Conjecture to non‐complete graphs due to DeBiasio–Kamel–McCourt–Sheats.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Graph Theory Research
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 4
- Publication date
- 20 August 2026
- Language
- EN