On The Restricted Size Ramsey Number

Abstract Let F , G , and H be simple graphs. We say F → ( G , H ) if for every 2-coloring of the edges of F there exists a monochromatic G or H in F . The Ramsey number r ( G , H ) is defined as min {| V ( F )|: F → ( G , H )}, while the restricted size Ramsey number r ∗( G , H ) is defined as min {| E ( F )|: F → ( G , H ), | V ( F ) | = r ( G , H )}. In this paper, we give lower and upper bounds for the restricted size Ramsey number for a path P 3 versus cycles Cn .