This paper describes a new technique referred to as
which improves the performance of BBMC, a leading state of the art exact maximum clique solver (MCP). It is based on watched literals employed by modern SAT solvers for Boolean constraint propagation. The paper proposes to watch two subgraphs of critical sets during MCP search to efficiently compute new steps and bounds. Reported results validate the approach as the size and density of problem instances rise, while achieving comparable performance in the general case.