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Julia Dandurand,
California State University, Northridge
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"Settling the Blazek-Koman Conjecture for k-page Book Drawings of Complete Graphs with at most 3k Vertices"
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Determining the crossing number of a graph, that is, the minimum
number of crossings among all drawings of the graph, is a problem in Discrete
Geometry. In the 60s, Blazek and Koman found k-page book drawings of
the complete graph with few crossings and conjectured that their
drawings had the minimum possible number of crossings.
This conjecture was recently settled for k = 2 but remains open for
larger values of k. This talk presents our work in proving the
conjecture when the ratio of the number of vertices to the number
of pages is small.