Fano Plane - Matroid Theory

Matroid Theory

Main article: Matroid theory

The Fano plane is one of the important examples in the structure theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular, graphic, and cographic ones.

If you break one line apart into three 2-point lines you obtain the "non-Fano configuration", which can be embedded in the real plane. It is another important example in matroid theory, as it must be excluded for many theorems to hold.