The pair-crossing number of a graph G, pcr(G), is the minimum possible number of pairs of edges that cross each other (possibly several times) in a drawing of G. It is known that there is a constant c ≥ 1/64 such that for every (not too sparse) graph G with n vertices and m edges pcr(G) ≥ c m3/n2. This bound is tight, up to the constant c. Here we show that c ≥ 1/34.2 if G is drawn without adjacent crossings.
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© Springer-Verlag Berlin Heidelberg 2014.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)