English

The tripartite-circle crossing number of graphs with two small partition classes

Combinatorics 2024-11-25 v2 Discrete Mathematics

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. The tripartite-circle crossing number of a tripartite graph is the minimum number of edge crossings among all its tripartite-circle drawings. We determine the exact value of the tripartite-circle crossing number of Ka,b,nK_{a,b,n}, where a,b2a,b\leq 2.

Keywords

Cite

@article{arxiv.2108.01032,
  title  = {The tripartite-circle crossing number of graphs with two small partition classes},
  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:2108.01032},
  year   = {2024}
}

Comments

22 pages, 11 figures. Added new results and revised throughout. Originally appeared in arXiv:1910.06963v1, now removed from arXiv:1910.06963v2