Clique covering the edges of a locally cobipartite graph (Q1567657)

A graph is locally cobipartite if the vertices of the neighbourhood of any vertex can be covered by at most two cliques. The authors prove that a locally cobipartite graph on \(n\) vertices has a family of at most \(n\) cliques that cover its edges. This result supports Opsut's conjecture that the competition number of a locally cobipartite graph is at most \(2\).