Improved lower bounds for the 2-page crossing numbers of Km,n and Kn via semidefinite programming

• Main Authors: Klerk, E. de., Pasechnik, Dmitrii V.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/96333; http://hdl.handle.net/10220/10215
• Institution: Nanyang Technological University

It has long been conjectured that the crossing numbers of the complete bipartite graph $K_{m,n}$ and of the complete graph $K_n$ equal $Z(m,n):=\bigl\lfloor\frac{n}{2}\bigr\rfloor \bigl\lfloor\frac{n-1}{2}\bigr\rfloor \bigl\lfloor\frac{m}{2}\bigr\rfloor \bigl\lfloor\frac{m-1}{2}\bigr\rfloor$ and $Z(...