On clique-gated graphs

Hagauer and Klavžar (1996) introduced clique-gated graphs as a generalization of quasi-median graphs. In their paper they proposed a problem whether a clique-gated graph can include any induced C5. This note gives a positive answer constructing such a graph. Moreover, a graph on 15 vertices which is a subgraph of every clique-gated including an induced C5 is found.