Maximal-clique partitions of interval graphs
Ma Shaohan, W. D. Wallis · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1988
Abstract It is shown that if an interval graph possesses a maximal-clique partition then its clique covering and clique partition numbers are equal, and equal to the maximal-clique partition number. Moreover an interval graph has such a partition if and only if all its maximal cliques are edge-disjoint.