## On maximal clique irreducible graphs.(English)Zbl 0735.05052

Summary: A graph $$G$$ is said to be maximal clique irreducible if each maximal clique in $$G$$ contains an edge which is not contained in any other maximal clique of $$G$$. In 1981, Opsut and Roberts proved that any interval graph is maximal clique irreducible. We generalize their result and consider the question of characterizing maximal clique irreducible graphs.

### MSC:

 05C35 Extremal problems in graph theory

### Keywords:

maximal clique irreducible graphs