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 . 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