English

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 K3,3,3K_{3,3,3} 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

R2 v1 2026-06-21T13:55:13.780Z