New lower bounds on the size-Ramsey number of a path
Combinatorics
2021-11-05 v4
Abstract
We prove that for all graphs with at most edges there exists a 2-coloring of the edges such that every monochromatic path has order less than . This was previously known to be true for graphs with at most edges. We also improve on the best-known lower bounds in the -color case.
Cite
@article{arxiv.1909.06354,
title = {New lower bounds on the size-Ramsey number of a path},
author = {Deepak Bal and Louis DeBiasio},
journal= {arXiv preprint arXiv:1909.06354},
year = {2021}
}
Comments
18 pages, 5 figures; (v4) Updated in response to referee comments. Simplified the proof of Lemma 2.4. Improved the exposition of the proofs of Lemma 2.16 and Theorem 1.1. (v3) Significantly reorganized the proof of the main theorem (v2) Minor edits