A complete classification of the [formula omitted]-configurations with at least three [formula omitted]-graphs.

The class of ( ( n + 1 2 ) n − 1 ( n + 1 3 ) 3 ) -configurations which contain at least n − 2 K n -graphs coincides with the class of so called systems of triangle perspectives i.e. of configurations which contain a bundle of n − 2 Pasch configurations with a common line. For n = 5 the class consists of all binomial partial Steiner triple systems on 15 points, that contain at least three K 5 -graphs. In this case a complete classification of respective configurations is given and their automorphisms are determined. [ABSTRACT FROM AUTHOR]