Work

A counterexample to the coarse Menger conjecture

Year: 2025

Type: article

Abstract: Menger's well-known theorem from 1927 characterizes when it is possible to find k vertex-disjoint paths between two sets of vertices in a graph G . Recently, Georgakopoulos and Papasoglu and, independently, Albrechtsen, Huynh, Jacobs, Knappe and Wollan conjectured a coarse analogue of Menger's theorem, when the k paths are required to be pairwise at some distance at least d . The result is known for k ≤ 2 , but we will show that it is false for all k ≥ 3 , even if G is constrained to have maximum degree at most three. We also give a simpler proof of the result when k = 2 .

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2025.01.004

Authors: Tung Nguyen, Alex Scott, Paul Seymour

Institutions: Princeton University, University of Oxford

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,150

Funders: National Science Foundation, National Sleep Foundation, Engineering and Physical Sciences Research Council, Air Force Office of Scientific Research