On some Ramsey Numbers for Quadrilaterals

Abstract

We will prove that $R(C_4, C_4, K_4-e)=16$. This fills one of the gaps in the tables presented in a 1996 paper by Arste et al. Moreover by using computer methods we improve lower and upper bounds for some other multicolor Ramsey numbers involving quadrilateral $C_4$. We consider $3$ and $4$-color numbers, our results improve known bounds.