The minimal density of triangles in tripartite graphs

Details The minimal density of triangles in tripartite graphs The minimal density of triangles in tripartite graphs

2009-10-07

arxiv.org/abs/0910.1237v1

Mathematics

Combinatorics

44 pages including 12 page appendix of C++ code

Scientific paper

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 $K_{3,3,3}$ has minimal triangle density among all weighted tripartite graphs with prescribed edge densities.

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