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Improved lower bounds for the 2-page crossing numbers of K(m,n) and K(n) via semidefinite programming

Etienne De Klerk(e.deklerk***at***uvt.nl)
Dmitrii V. Pasechnik(dima***at***ntu.edu.sg )

Abstract: The crossing number of a graph is the minimal number of edge crossings achievable in a drawing of the graph in the plane. The crossing numbers of complete and complete bipartite graphs are long standing open questions. In a 2-page drawing of a graph, all vertices are drawn on a circle, and no edge may cross the circle. It has been conjectured that the 2-page and normal crossing numbers coincide for complete and complete bipartite graphs. In this paper, we derive improved lower bounds on the 2-page crossing numbers for these two classes of graphs via semidefinite programming.

Keywords: 2-page crossing number, book crossing number, semidefinite programming, maximum cut, Goemans-Williamson max-cut bound

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Combinatorial Optimization (Graphs and Matroids )

Category 3: Combinatorial Optimization

Citation: Preprint, Tilburg University, October 2011.

Download: [PDF]

Entry Submitted: 10/19/2011
Entry Accepted: 10/19/2011
Entry Last Modified: 10/19/2011

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