Kelmans–Seymour conjecture

Statement

In graph theory, the Kelmans–Seymour conjecture states that every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph $K_{5}$. 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.