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Artificial Intelligence and Machine Learning

A generalized implicit enumeration algorithm for graph coloring

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A generalized algorithm for graph coloring by implicit enumeration is formulated. A number of backtracking sequential methods are discussed in terms of the generalized algorithm. Some are revealed to be partially correct and inexact. A few corrections to the invalid algorithms, which cause these algorithms to guarantee optimal solutions, are proposed. Finally, some computational results and remarks on the practical relevance of improved implicit enumeration algorithms are given.

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