The minimal density of triangles in tripartite graphs
Combinatorics
2019-02-20 v1
Abstract
We determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends a previous result of Bondy, Shen, Thomass\'e and Thomassen characterizing those edge densities guaranteeing the existence of a triangle in a tripartite graph. To be precise we show that a suitably weighted copy of the graph formed by deleting a certain 9-cycle from has minimal triangle density among all weighted tripartite graphs with prescribed edge densities.
Keywords
Cite
@article{arxiv.0910.1237,
title = {The minimal density of triangles in tripartite graphs},
author = {Rahil Baber and J. Robert Johnson and John Talbot},
journal= {arXiv preprint arXiv:0910.1237},
year = {2019}
}
Comments
44 pages including 12 page appendix of C++ code