Bounding the tripartite-circle crossing number of complete tripartite graphs
Date
2021-10
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Publisher
Wiley
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 Km,n,p and the exact value for K2,2,n. 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.
Description
This article is published open access in the Journal of Graph Theory, also available at https://doi.org/10.1002/jgt.22763. Made available under the CC BY-NC-ND 4.0 license.
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Journal Article
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Citation
Camacho, C., Fernandez-Merchant, S., Jelic Milutinovic, M., Kirsch, R., Kleist, L., Matson, E. B., and White, J., Bounding the tripartite-circle crossing number of complete tripartite graphs, J. Graph Theory. 2022; 100: 5– 27. https://doi.org/10.1002/jgt.22763