Practical examples/applications of independent sets in hypergraphs?

Question

A hypergraph $H$ is a collection of subsets of a set $V$. And $V$ is called its vertex-set. And those subsets are called its edges (or hyperedges.) And an independent set of $H$ is a subset $I$ of $V$ such that no edge of $H$ is contained in $I$.

I wonder if there are any examples/applications of independent sets in hypergraphs that are understandable to public who do not know lots of mathematics?
For example, an example I made is that each vertex of $V$ stands for a person, an edge stands for a small group. So each person may belong to some groups. So an independent set corresponds to some people that none of them form a group.
I wonder are there more fancy examples/applications corresponding to independent sets?

Answer 1

Much of Ramsey theory deals with independent sets in some specific family of hypergraphs. Here are some examples from this line of thinking that are all somewhat mathematical, but not too mathematically sophisticated:

• Take a game of tic-tac-toe. (Or gomoku, if you prefer a game with style.) If the game hasn't ended in a win for either player, then each player's marks form an independent set in a hypergraph: the hypergraph where each edge is a winning line in tic-tac-toe.
• A Golomb ruler might be easy to describe even to a nonmathematical audience: you pick a set of $n$ marks at integer points on a ruler such that the $\binom n2$ distances between the marks are different. This is an independent set in a hypergraph: one which has an edge $\{a,b,c,d\}$ whenever $a-b = c-d$ (and an edge $\{a,b,c\}$ whenever $a-b = b-c$).
• A set of points in the plane with no three of them collinear (which we could word-problem into "$n$ people standing so that each of them can see all $n-1$ other people without their view blocked") is an independent set in an infinite hypergraph.