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  "body": "\n## Statement\n\nIn graph theory, the **Kelmans–Seymour conjecture** states that every 5-vertex-connected graph that is not [[planar|029JQEK15B]] contains a subdivision of the 5-vertex [[complete graph|03WKB2H474]] $K_{5}$. It is named for Paul Seymour and Alexander Kelmans, who independently described the conjecture; Seymour in 1977 and Kelmans in 1979. A proof was announced in 2016, and published in four papers in 2020.\n",
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