New Lower Bounds on the Multicolor Ramsey Numbers rk(C4)

The multicolor Ramsey number rk(C4) is the smallest integer n for which any k-coloring of the edges of the complete graph Kn must produce a monochromatic 4-cycle. It was proved earlier that rk(C4)⩾k2−k+2 for k−1 being a prime power. In this note we establish rk(C4)⩾k2+2 for k being an odd prime power.