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Maximum Clique Problem(MCP) is one of the 21 original NP--complete problemsenumerated by Karp in 1972. In recent years a large number of exact methods tosolve MCP have been appeared(Babel, Wood, Kumlander, Fahle, Li, Tomita andetc). Most of them are branch and bound algorithms that use branching ruleintroduced by Balas and Yu and based on coloring heuristics to establish anupper bound on the clique number. They differ from each other primarily invertex preordering and vertex coloring methods. Current methods of worst caserunning time analysis for branch and bound algorithms do not allow to providetight upper bounds. This motivates the study of lower bounds for suchalgorithms. We prove 2^(n\5) lower bound for group of MCP algorithms based onusage of coloring heuristics.

On the Complexity of Maximum Clique Algorithms: usage of coloring heuristics leads to the 2^(n\5) algorithm running time lower bound