Work

A proof of a conjecture of Erdős and Gyárfás on monochromatic path covers

Year: 2025

Type: article

Abstract: In 1995, Erdős and Gyárfás proved that in every 2-edge-coloured complete graph on n vertices, there exists a collection of 2 n monochromatic paths, all of the same colour, which cover the entire vertex set. They conjectured that it is possible to replace 2 n by n . We prove this to be true for all sufficiently large n .

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2025.10.007

Authors: Alexey Pokrovskiy, Leo Versteegen, Ella Williams

Institution: University College London

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: London Mathematical Society, Heilbronn Institute for Mathematical Research