Bounding the tripartite-circle crossing number of complete tripartite graphs
Combinatorics
2023-06-30 v2
Abstract
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. We present upper and lower bounds on the minimum number of crossings in tripartite-circle drawings of . In contrast to 1- and 2-circle drawings, which may attain the Harary-Hill bound, our results imply that balanced restricted 3-circle drawings of the complete graph are not optimal.
Keywords
Cite
@article{arxiv.1910.06963,
title = {Bounding the tripartite-circle crossing number of complete tripartite graphs},
author = {Charles Camacho and Silvia Fernández-Merchant and Marija Jelić Milutinović and Rachel Kirsch and Linda Kleist and Elizabeth Bailey Matson and Jennifer White},
journal= {arXiv preprint arXiv:1910.06963},
year = {2023}
}
Comments
21 pages, 13 figures. arXiv:1910.06963v1 was split into doi:10.1002/jgt.22763=arXiv:1910.06963v2 and arXiv:2108.01032, with K22n result in the latter. Removed K22n from JGT abstract to reflect the published JGT paper