{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T03:21:07Z","timestamp":1791343267189,"version":"4.3.1"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>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, which 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 the early 1990s.<\/jats:p>","DOI":"10.1137\/070687256","type":"journal-article","created":{"date-parts":[[2009,5,20]],"date-time":"2009-05-20T18:27:35Z","timestamp":1242844055000},"page":"909-939","source":"Crossref","is-referenced-by-count":95,"title":["Clique-Width is NP-Complete"],"prefix":"10.1137","volume":"23","author":[{"given":"Michael R.","family":"Fellows","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frances A.","family":"Rosamond","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Udi","family":"Rotics","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Szeider","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,5,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/0608024"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1995.1009"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"R. Boliac and V. Lozin,\n                      On the clique-width of graphs in hereditary classes\n                      , in Algorithms and Computation, Lecture Notes in Comput. Sci. 2518, Springer-Verlag, Berlin, 2002, pp. 44\u201354.","DOI":"10.1007\/3-540-36136-7_5"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-004-1154-6"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-005-1199-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539701385351"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"D. G. Corneil, M. Habib, J.M. Lanlignel, B. A. Reed, and U. Rotics,\n                      Polynomial time recognition of clique-width $\\leq 3$ graphs (extended abstract)\n                      , in LATIN 2000: Theoretical Informatics, 4th Latin American Symposium, G. H. Gonnet, D. Panario, and A. Viola, eds., Lecture Notes in Comput. 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