A Better Bound for the Pair-Crossing Number

Chapter

Abstract

The crossing number cr(G) of a graph G is the minimum possible number of edge crossings in a drawing of G, and the pair-crossing number pair-cr(G) is the minimum possible number of crossing pairs of edges in a drawing of G. Clearly, pair-cr(G) ≤ cr(G). We show that for any graph G, \(\mathrm{cr}(G) = O(\text{ pair-cr}{(G){}^{7/4}\log }^{3/2}(\text{ pair-cr}(G)))\).

Notes

Acknowledgements

The author is very grateful to the anonymous referee for pointing out several typos and errors in the calculation, and for some other useful remarks.

The author was supported by OTKA Grants K-83767 and K-102029.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Rényi InstituteHungarian Academy of SciencesBudapestHungary

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