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 - <p style="text-align: justify;">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.</p>