A Crossing Lemma for the pair-crossing number

被引：1
|
作者：
Ackerman, Eyal [1 ]
Schaefer, Marcus [2 ]
机构：
[1] Dept. Math., Physics, and Comp. Sci, University of Haifa at Oranim, Tivon, Israel
[2] School of Computing, DePaul University, Chicago,IL,60604, United States
来源：
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | 2014年 / 8871卷
关键词：
Crossing number - Graph G;
D O I：
10.1007/978-3-662-45803-7_19
中图分类号：
学科分类号：
摘要：
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. © Springer-Verlag Berlin Heidelberg 2014.
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页码：222 / 233
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