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.

引用

页码：222 / 233

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