Triple crossing numbers of graphs

Hiroyuki Tanaka; Masakazu Teragaito

Triple crossing numbers of graphs

Combinatorics 2012-01-16 v2

Authors: Hiroyuki Tanaka , Masakazu Teragaito

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.

Keywords

graph pebbling graph theory graph coloring

Cite

@article{arxiv.1002.4231,
  title  = {Triple crossing numbers of graphs},
  author = {Hiroyuki Tanaka and Masakazu Teragaito},
  journal= {arXiv preprint arXiv:1002.4231},
  year   = {2012}
}

Comments

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

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