Intersecting two-element set family
= Intersecting two-element set family
A pairwise <intersecting family> of two-element sets is contained in a <star graph> or in the three <edges> of a <triangle in a graph>. If two members are $\{a,b\},\{a,c\}$ and a third avoids $a$, the third must be $\{b,c\}$. Every member meeting all three belongs to that triangle.