Crossing Number Is Hard for Cubic Graphs

It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP-hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP-hard to determine the crossing number of a simple cubic graph. In particular, this implies that the minor-monotone version of crossing number is also NP-hard, which has been open till now.

• Type: Conference
• Year: 2004
• Where: MFCS
• Authors: Petr Hlinený
• Keywords: MFCS 2004, NP-hard Problem, Parallel Edges, Simple Cubic Graph