Nearly-linear monotone paths in edge-ordered graphs
Combinatorics
2019-09-20 v3
Abstract
How long a monotone path can one always find in any edge-ordering of the complete graph ? This appealing question was first asked by Chv\'atal and Koml\'os in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was . In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length .
Keywords
Cite
@article{arxiv.1809.01468,
title = {Nearly-linear monotone paths in edge-ordered graphs},
author = {Matija Bucic and Matthew Kwan and Alexey Pokrovskiy and Benny Sudakov and Tuan Tran and Adam Zsolt Wagner},
journal= {arXiv preprint arXiv:1809.01468},
year = {2019}
}