当前位置: X-MOL 学术Discret. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the size Ramsey number of all cycles versus a path
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-02-11 , DOI: 10.1016/j.disc.2021.112322
Deepak Bal , Ely Schudrich

We say G(C,Pn) if GE(F) contains an n-vertex path Pn for any spanning forest FG. The size Ramsey number Rˆ(C,Pn) is the smallest integer m such that there exists a graph G with m edges for which G(C,Pn). Dudek, Khoeini and Prałat proved that for sufficiently large n, 2.0036nRˆ(C,Pn)31n. In this note, we improve both the lower and upper bounds to 2.066nRˆ(C,Pn)5.25n+O(1). Our construction for the upper bound is completely different than the one considered by Dudek, Khoeini and Prałat. We also have a computer assisted proof of the upper bound Rˆ(C,Pn)7519n+O(1)<3.947n.



中文翻译:

关于所有循环的大小Ramsey数与路径

我们说 GCPñ 如果 G-ËF 包含一个 ñ-顶点路径 Pñ 对于任何跨越森林 FG。大小拉姆齐数[RˆCPñ 是最小的整数 这样就存在一个图 G 的边缘 GCPñ。Dudek,Khoeini和Prałat证明了足够大ñ20036ñ[RˆCPñ31ñ。在本说明中,我们将上限和下限都提高了2066ñ[RˆCPñ525ñ+Ø1个我们的上限结构与Dudek,Khoeini和Prałat所考虑的完全不同。我们还有上限的计算机辅助证明[RˆCPñ7519ñ+Ø1个<3947ñ

更新日期:2021-02-12
down
wechat
bug