1Oregon State University, Corvallis, USA 2Department of Mathematics, California State University, Northridge, USA 3London School of Economics, London, UK 4Department of Computer Science, Technische Universität Braunschweig, Germany 5Department of Mathematics, Alfred University, New York, USA 6University of Belgrade, Serbia 7Department of Mathematics, Saint Vincent College, Latrobe, USA
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 515-520
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Charles Anthony Camacho; Silvia Fernández-Merchant; Rachel Kirsch; Linda Kleist; Elizabeth Bailey Matson; Marija Jelić Milutinović; Jennifer White; Charles Anthony Camacho; Silvia Fernández-Merchant; Rachel Kirsch; Linda Kleist; Elizabeth Bailey Matson; Marija Jelić Milutinović; Jennifer White. Bounding the tripartite-circle crossing number of complete tripartite graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 515-520. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a25/
@article{AMUC_2019_88_3_a25,
author = {Charles Anthony Camacho and Silvia Fern\'andez-Merchant and Rachel Kirsch and Linda Kleist and Elizabeth Bailey Matson and Marija Jeli\'c Milutinovi\'c and Jennifer White and Charles Anthony Camacho and Silvia Fern\'andez-Merchant and Rachel Kirsch and Linda Kleist and Elizabeth Bailey Matson and Marija Jeli\'c Milutinovi\'c and Jennifer White},
title = { Bounding the tripartite-circle crossing number of complete tripartite graphs},
journal = {Acta mathematica Universitatis Comenianae},
pages = {515--520},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a25/}
}
TY - JOUR
AU - Charles Anthony Camacho
AU - Silvia Fernández-Merchant
AU - Rachel Kirsch
AU - Linda Kleist
AU - Elizabeth Bailey Matson
AU - Marija Jelić Milutinović
AU - Jennifer White
AU - Charles Anthony Camacho
AU - Silvia Fernández-Merchant
AU - Rachel Kirsch
AU - Linda Kleist
AU - Elizabeth Bailey Matson
AU - Marija Jelić Milutinović
AU - Jennifer White
TI - Bounding the tripartite-circle crossing number of complete tripartite graphs
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 515
EP - 520
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a25/
ID - AMUC_2019_88_3_a25
ER -
%0 Journal Article
%A Charles Anthony Camacho
%A Silvia Fernández-Merchant
%A Rachel Kirsch
%A Linda Kleist
%A Elizabeth Bailey Matson
%A Marija Jelić Milutinović
%A Jennifer White
%A Charles Anthony Camacho
%A Silvia Fernández-Merchant
%A Rachel Kirsch
%A Linda Kleist
%A Elizabeth Bailey Matson
%A Marija Jelić Milutinović
%A Jennifer White
%T Bounding the tripartite-circle crossing number of complete tripartite graphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 515-520
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a25/
%F AMUC_2019_88_3_a25
A tripartite-circle drawing of the complete tripartite graph $K_{m,n,p}$ is a drawing in the plane, where each part of the 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 $K_{m,n,p}$ %and $\crN{3}(K_{n,n,n})$and the exact value for $K_{2,2,n}$. In contrast to 1- and 2-circle drawings which may attain the Harary-Hill bound, our results imply that optimal drawings of the complete graph do not contain balanced 3-circle drawings as subdrawings that do not cross any of the remaining edges.
