Inducibility of Four‐Vertex Tournaments

ABSTRACT We determine the inducibility of all tournaments with at most four vertices together with the extremal constructions. The four‐vertex tournament containing an oriented and one source vertex has a particularly interesting extremal construction, first conjectured by Bożyk, Grzesik, and Kielak. It is an unbalanced blow‐up of an edge, where the sink vertex is replaced by a quasi‐random tournament and the source vertex is iteratively replaced by a copy of the construction itself.