Aichholzer, Oswin; Matematčni kolokvij maj 2012

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On the 2-page book crossing number of the complete graph

Oswin Aichholzer

Institute for Software Technology, Graz University of Technology

10. maj 2012

A 2-page book drawing of the complete graph Kn is a drawing where all the vertices are on a line l (the spine) and each edge is fully contained in one of the two half-planes (pages) defined by l. The 2-page crossing number of Kn is the minimum number of crossings determined by a 2-page book drawing of Kn. In this talk we will provide the exact bound for this 2-page crossing number and thus provide a significant step towards proving Hill's conjecture on the crossing number of the complete graph Kn. This is joint work with Bernardo M. Abrego, Silvia Fernandez-Merchant, Pedro Ramos, and Gelasio Salazar.

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