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This paper begins by exploring some old and new results about minimum numbersof monochromatic triangles in $2$-colorings of complete graphs, both in thedisjoint and non-disjoint cases. We then extend the theory, by defining line$2$-colorings of configurations of points and lines and considering the minimumnumber of non-disjoint monochromatic triangles. We compute specific examplesfor notable symmetric $v_{3}$ configurations before considering a generalresult regarding the addition or connected sum of configurations throughincidence switches. The paper finishes by considering the maximal number ofmutually intersecting lines and how this relates to the minimum number oftriangles given a line $2$-coloring of a symmetric $v_{3}$ configuration.

Minimum numbers of monochromatic triangles in line $2$-colorings of $v_{3}$ configurations of points and lines