The clique operator \(K\) maps a graph \(G\) into its clique graph, which is the intersection graph of the (maximal) cliques of \(G\). Recognizing clique graphs is a problem known to be in NP, but no polynomial time algorithm or proof of NP-completeness is known. In this note we prove that this recognition problem can be reduced to the case of graphs of diameter at most two.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.