English

On edge-ordered graphs with linear extremal functions

Combinatorics 2024-07-12 v2

Abstract

The systematic study of Tur\'an-type extremal problems for edge-ordered graphs was initiated by Gerbner et al. in 2020. Here we characterize connected edge-ordered graphs with linear extremal functions and show that the extremal function of other connected edge-ordered graphs is Ω(nlogn)\Omega(n\log n). This characterization and dichotomy are similar in spirit to results of F\"uredi et al. (2020) about vertex-ordered and convex geometric graphs. We also extend the study of extremal function of short edge-ordered paths by Gerbner et al. to some longer paths.

Keywords

Cite

@article{arxiv.2309.10558,
  title  = {On edge-ordered graphs with linear extremal functions},
  author = {Gaurav Kucheriya and Gábor Tardos},
  journal= {arXiv preprint arXiv:2309.10558},
  year   = {2024}
}

Comments

20 pages, 5 figures, 1 table

R2 v1 2026-06-28T12:26:01.543Z