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Strong perfect graph theorem
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{{Short description|Perfect graphs have neither odd holes nor odd antiholes}} In [[graph theory]], the '''strong perfect graph theorem''' is a [[forbidden graph characterization]] of the [[perfect graph]]s as being exactly the graphs that have neither odd holes (odd-length [[induced cycle]]s of length at least 5) nor odd antiholes (complements of odd holes). It was [[conjecture]]d by [[Claude Berge]] in 1961. A [[mathematical proof|proof]] by [[Maria Chudnovsky]], [[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]], and [[Robin Thomas (mathematician)|Robin Thomas]] was announced in 2002<ref>{{harvtxt|Mackenzie|2002}}; {{harvtxt|Cornuéjols|2002}}.</ref> and published by them in 2006. The proof of the strong perfect graph theorem won for its authors a $10,000 prize offered by [[Gérard Cornuéjols]] of Carnegie Mellon University<ref>{{harvtxt|Mackenzie|2002}}.</ref> and the 2009 [[Fulkerson Prize]].<ref>{{citation | date = December 2011 | journal = Notices of the American Mathematical Society | pages = 1475–1476 | title = 2009 Fulkerson Prizes | url = http://www.ams.org/notices/201011/rtx101101475p.pdf}}.</ref>
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