MathDB

We call

A_{1},A_{2},A_{3}

mangool iff there is a permutation

\pi

that

A_{\pi(2)}\not\subset A_{\pi(1)},A_{\pi(3)}\not\subset A_{\pi(1)}\cup A_{\pi(2)}

. A good family is a family of finite subsets of

\mathbb N

X,A_{1},A_{2},\dots,A_{n}

. To each goo family we correspond a graph with vertices

\{A_{1},A_{2},\dots,A_{n}\}

. Connect

A_{i},A_{j}

iff

X,A_{i},A_{j}

are mangool sets. Find all graphs that we can find a good family corresponding to it.

Problem Statement