CliSAT: A new exact algorithm for hard maximum clique problems

•A new exact combinatorial branch-and-bound algorithm for the maximum clique problem (MCP) is designed.•The proposed algorithm exploits a new filtering technique to effectively reduce the branching tree.•The proposed algorithm enhances current colour-based and SAT techniques to effectively reduce the branching tree.•Extensive tests show that the algorithm outperforms the state-of-the-art approaches in some cases by several orders of magnitude.