New methods to color the vertices of a graph
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Forbidden subgraphs implying the MIN-algorithm gives a maximum independent set
Discrete Mathematics
A survey of local search methods for graph coloring
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
Extended and discretized formulations for the maximum clique problem
Computers and Operations Research
Cliques with maximum/minimum edge neighborhood and neighborhood density
Computers and Operations Research
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We consider the problem of determining the size of a maximum clique in a graph, also known as the clique number. Given any method that computes an upper bound on the clique number of a graph, we present a sequential elimination algorithm which is guaranteed to improve upon that upper bound. Computational experiments on DIMACS instances show that, on average, this algorithm can reduce the gap between the upper bound and the clique number by about 60%. We also show how to use this sequential elimination algorithm to improve the computation of lower bounds on the clique number of a graph.