  A triangle-free graph G is called k-existentially complete if for every
induced k-vertex subgraph H of G, every extension of H to a (k+1)-vertex
triangle-free graph can be realized by adding another vertex of G to H. Cherlin
asked whether k-existentially complete triangle-free graphs exist for every k.
Here we present known and new constructions of 3-existentially complete
triangle-free graphs.
