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Volume 32, Issue 1
Triple Crossing Numbers of Graphs

Tanaka Hiroyuki & Teragaito Masakazu

DOI: 10.13447/j.1674-5647.2016.01.01

Commun. Math. Res., 32 (2016), pp. 1-38.

Published online: 2021-03

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  • Abstract

We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.

  • Keywords

crossing number, triple crossing number, complete multipartite graph.

  • AMS Subject Headings

05C10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-1, author = {Hiroyuki , Tanaka and Masakazu , Teragaito}, title = {Triple Crossing Numbers of Graphs}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {1}, pages = {1--38}, abstract = {

We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.01.01}, url = {http://global-sci.org/intro/article_detail/cmr/18660.html} }
TY - JOUR T1 - Triple Crossing Numbers of Graphs AU - Hiroyuki , Tanaka AU - Masakazu , Teragaito JO - Communications in Mathematical Research VL - 1 SP - 1 EP - 38 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.01.01 UR - https://global-sci.org/intro/article_detail/cmr/18660.html KW - crossing number, triple crossing number, complete multipartite graph. AB -

We introduce the triple crossing number, a variation of the crossing number, of a graph, which is the minimal number of crossing points in all drawings of the graph with only triple crossings. It is defined to be zero for planar graphs, and to be infinite for non-planar graphs which do not admit a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs which include all complete graphs.

Hiroyuki , Tanaka and Masakazu , Teragaito. (2021). Triple Crossing Numbers of Graphs. Communications in Mathematical Research . 32 (1). 1-38. doi:10.13447/j.1674-5647.2016.01.01
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