Clique-Width is NP-Complete

نویسندگان

  • Michael R. Fellows
  • Frances A. Rosamond
  • Udi Rotics
  • Stefan Szeider
چکیده

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 such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. 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 NP-complete. This solves a problem that has been open since the introduction of clique-width in

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عنوان ژورنال:
  • SIAM J. Discrete Math.

دوره 23  شماره 

صفحات  -

تاریخ انتشار 2009