Browsing University of Waterloo by Subject "crossing number"

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2-crossing critical graphs with a V8 minor

Austin, Beth Ann (University of Waterloo, 2012-01-17)

The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a ...
On the Crossing Numbers of Complete Graphs

Pan, Shengjun (University of Waterloo, 2006)

In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of Kn must be a triangle (for n ≥ 3). We prove that, ...