One example: A 3-uniform hypergraph is the natural way to model the variable/clause structure of a 3-Sat instance. Since 3-Sat is one of the most important algorithmic problems in computational complexity theory, hypergraphs play an important role there.

For just one of many possible examples, take a look at the following paper of Feige, Kim, and Ofek:

 https://www.microsoft.com/en-us/research/wp-content/uploads/2017/03/unsat.pdf

One example: A 3-uniform hypergraph is the natural way to model the variable/clause structure of a 3-Sat instance. Since 3-Sat is one of the most important algorithmic problems in computational complexity theory, hypergraphs play an important role there.

For just one of many possible examples, take a look at the paper of Feige, Kim, and Ofek:  Witnesses for non-satisfiability of dense random 3CNF formulas.

One example: A 3-uniform hypergraph is the natural way to model the variable/clause structure of a 3-Sat instance. Since 3-Sat is one of the most important algorithmic problems in computational complexity theory, hypergraphs play an important role there.

For just one of many possible examples, take a look at the following paper of Feige, Kim, and Ofek:

http://research.microsoft.com/en-us/um/redmond/groups/theory/feige/homepagefiles/witness5.9.06.pdf

One example: A 3-uniform hypergraph is the natural way to model the variable/clause structure of a 3-Sat instance. Since 3-Sat is one of the most important algorithmic problems in computational complexity theory, hypergraphs play an important role there.

For just one of many possible examples, take a look at the following paper of Feige, Kim, and Ofek:

https://www.microsoft.com/en-us/research/wp-content/uploads/2017/03/unsat.pdf