A tetrahedron-free graph is a graph containing no 
-subgraphs (i.e., a graph with graph
tetrahedron count of 0).
Some interesting tetrahedron-free graphs are summarized in the following table, where 
denotes the chromatic number.
| vertex count |  | graph |
| 61 | 5 | 61-de Grey graph |
| 372 | 5 | 372-Voronov-Neopryatnaya-Dergachev graph |
| 972 | 5 | 972-Voronov-Neopryatnaya-Dergachev graph |
| 21217 | 6 | 21217-Haugstrup graph |
