路径的尺寸-拉姆齐数的新下界
组合数学
2021-11-05 v4
摘要
我们证明，对于所有边数不超过 的图，存在一种边的 2-着色，使得每条单色路径的阶小于 。此前已知这对边数不超过 的图成立。我们还改进了 -着色情形下已知的最佳下界。
引用
@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}
}
备注
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