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Date: 2-8-2016
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Date: 3-3-2022
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Date: 3-8-2016
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The clique covering number of a graph is the minimum number of cliques in needed to cover the vertex set of . Since involves the minimum number of cliques, only maximal cliques need be considered (since non-maximal cliques could not yield a clique cover of smaller size).
The clique covering number is also given by
where is the chromatic number of a graph and is the graph complement of .
The clique covering number of some classes of graph are given by
graph | |
complete -partite graph with | |
complete graph | 1 |
cycle graph |
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REFERENCES
West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 226, 2000.
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