Document Type
Preprint
Publication Date
5-1-2021
Journal / Book Title
Discrete Mathematics
Abstract
We say G→(C,Pn) if G−E(F) contains an n-vertex path Pn for any spanning forest F⊂G. 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, 2.0036n≤Rˆ(C,Pn)≤31n. In this note, we improve both the lower and upper bounds to 2.066n≤Rˆ(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 [Figure presented].
DOI
10.1016/j.disc.2021.112322
MSU Digital Commons Citation
Bal, Deepak and Schudrich, Ely, "On the size Ramsey number of all cycles versus a path" (2021). Department of Mathematics Faculty Scholarship and Creative Works. 242.
https://digitalcommons.montclair.edu/mathsci-facpubs/242
Rights
© The authors. Released under the CC BY-ND license (International 4.0)
Published Citation
Bal, D., & Schudrich, E. (2021). On the size Ramsey number of all cycles versus a path. Discrete Mathematics, 344(5), 112322.