On Regressive Ramsey Numbers

We prove the following relation between regressive and classical Ramsey numbers Rregn(n+2)=Rn−1(n)+2. This is used to compute Rreg3(5)=8, Rreg4 (6)=15, and Rreg5(7)⩾36. We prove that Rx+k2(4)⩽2k+1(3+k)−(k+1), and use this to compute R2reg(5)=15. Finally, we provide the bounds 195⩽Rreg2(6)⩽ 5·242+239−2.