Corpus ID: 18336611

Clique , independent set , and graph coloring

@inproceedings{Pattillo2010CliqueI,
  title={Clique , independent set , and graph coloring},
  author={Jeffrey Pattillo and S. Butenko},
  year={2010}
}
This article introduces the closely related maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems. The survey includes some of the most important results concerning these problems, including their computational complexity, known bounds, mathematical programming formulations, and exact and heuristic algorithms to solve them. 
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References

SHOWING 1-10 OF 112 REFERENCES
The maximum clique problem
TLDR
A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed. Expand
On cliques in graphs
A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliquesExpand
A fast algorithm for the maximum clique problem
TLDR
A branch-and-bound algorithm for the maximum clique problem--which is computationally equivalent to the maximum independent (stable) set problem--is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy. Expand
Upper Bounds on the Order of a Clique of a Graph
This note presents an upper bound on the order of a largest complete subgraph (a clique) of a graph. Other upper bounds are given and the relationship between this bound and an existing bound isExpand
An exact method for graph coloring
TLDR
These algorithms are the first to the knowledge to solve the COLOR02 instance 4-Inser_3 with an exact method and are useful to solve more quickly than other exact algorithms instances with small linearwidth, such as mug graphs. Expand
A Column Generation Approach for Graph Coloring
TLDR
This work uses a column generation method for implicit optimization of the linear program at each node of the branch-and-bound tree to solve small to moderate size problems quickly. Expand
A branch-and-cut algorithm for the maximum cardinality stable set problem
TLDR
A branch-and-cut algorithm for the Maximum Cardinality Stable Set problem is proposed and a computational experience on the DIMACS benchmark graphs validates the effectiveness of the approach. Expand
Finding a Maximum Independent Set
TLDR
An algorithm is presented which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time and can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm. Expand
Finding a Maximum Clique in an Arbitrary Graph
TLDR
A new type of branch and bound procedure for finding a maximum clique in an arbitrary graph G, which discusses computational experience on randomly generated graphs with up to 400 vertices and 30,000 edges. Expand
A semidefinite programming-based heuristic for graph coloring
TLDR
A self-contained presentation of the role of the Lovasz @q-function in obtaining heuristics for the graph coloring problem is presented, which could be useful for coloring medium sized graphs as numerical results on DIMACS benchmark graphs indicate. Expand
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