Abstract: 
We are interested in a 3-coloring of the edges of large complete graphs minimizing the number of monochromatic triangles.
In this talk, we show how to combine Razborov's flag algebra method with other probabilistic and extremal techniques to 
obtain the extremal examples. This is joint work with Konrad Sperfeld (Rostock), Dan Kral, and Andrew Treglown (Prague).