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What is the crossing number problem? Why did it start? (see history – Turan’s brick
problem)
Actual answer is NP-Complete, however we can use good algorithms to find answers
sometimes, and also find bounds quickly
Complete bipartite graph – K(m, n), show examples below
Inequality, show proof – using Euler’s formula and expectation
Crossing number problem:
cr(G), the crossing number of a graph G, is the lowest number of edge crossings in a
graph.
K(3, 3)
(2 crossing: Petersen graph)
- this shows the method for representing a
complete bipartite graph with as few crossings as possible