Abstract
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.
2000 Math Subjects Classification: 05C10, 05C62, 68R10
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Hliněný, P. (2004). Crossing Number Is Hard for Cubic Graphs. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_60
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DOI: https://doi.org/10.1007/978-3-540-28629-5_60
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