On Graph Crossing Number and Edge Planarization

Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their endpoints. A crossing in such a drawing is a point where two such curves intersect. In the Minimum Crossing Number problem, the goal is to find a drawing of G with minimum number of crossings. The value of the optimal solution, denoted by OPT, is called the graph's crossing number. This is a very basic problem in topological graph theory, that has received a significant amount of attention, but is still poorly understood algorithmically. The best currently known efficient algorithm produces drawings with O(log2 n)

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Julia Chuzhoy, Yury Makarychev, Anastasios Sidiropoulos
• Keywords: CORR 2010, Education, Minimum Crossing Number, Minimum Planarization, N-vertex Graph