The minimal density of triangles in tripartite graphs
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 K3,3,3 has minimal triangle density among all weighted tripartite graphs with prescribed edge densities.
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