Ramsey Number of A Union of Stars Versus A Book

Abstract

The Ramsey number [Formula: see text] is the minimum integer [Formula: see text] such that any red-blue-coloring of [Formula: see text] contains either a red copy of [Formula: see text] or a blue copy of [Formula: see text]. In 2017, Zhang et al. showed that if [Formula: see text] and [Formula: see text], then [Formula: see text]. In this paper, we investigate the upper bound of the Ramsey number for a book and a star. Additionally, we extend the parameter range and present some exact values along with bounds for the Ramsey number [Formula: see text].