Complexity of products of even cycles (Q2908703)

Drawings of the Cartesian product \(C_r \times C_s\) of cycles or length \(r\) and \(s\) are considered. It is shown that the \textit{outerplanar crossing number} \(\nu_1(C_r \times C_s) \leq 4r^3 + 6r^2 - 8r\). The \textit{matching book thickness} \(\text{mbt}(G)\) is the minimum number of colors in an edge coloring of a layout of \(G\) such that same colored edges do not cross or are incident. It is shown that \(\text{mbt}(C_r \times C_s) = 4\) if both \(r\) and \(s\) are even and is \(5\) if precisely one of \(r\) or \(s\) is odd.