On the crossing number of \(K_{m,n}\)
Summary: The best lower bound known on the crossing number of the complete bipartite graph is \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor.\) We prove that \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2\) for sufficiently large \(m\) and \(n\).
scientific article; zbMATH DE number 1985383