Triple crossing numbers of graphs

2010/02/23 by Hiroyuki Tanaka, Tanaka, Hiroyuki, Masakazu Teragaito +1
Mathematics · #05C10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C10

paper · pdf · doi:10.48550/arxiv.1002.4231

34 pages, 53 figures: We reorganized the article and revised some arguments

arxiv created 2012/01/13 · arxiv updated 2012/01/16

Abstract

We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to be infinite unless a graph admits a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs including all complete graphs.

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