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Clique-width minimization is NP-hard.

Fellows, M. R. and Rosamond, F. A. and Rotics, U. and Szeider, S. (2006) 'Clique-width minimization is NP-hard.', 38th Annual ACM Symposium on Theory of Computing Seattle, Washington, USA, 21-23 May 2006.


Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in Monadic Second Order Logic with second-order quantification on vertex sets, that includes NP-hard problems) can be solved efficiently for graphs of small clique-width. It is widely believed that determining the clique-width of a graph is NP-hard; in spite of considerable efforts, no NP-hardness proof has been found so far. We give the first hardness proof. We show that the clique-width of a given graph cannot be absolutely approximated in polynomial time unless P=NP. We also show that, given a graph G and an integer k, deciding whether the clique-width of G is at most k is NPhy complete. This solves a problem that has been open since the introduction of clique-width in the early 1990s.

Item Type:Conference item (Paper)
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Record Created:23 Jan 2009
Last Modified:27 Nov 2009 14:08

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