---
tag: 709MQH16BE
kind: statement
role: proposition
name: Kelmans–Seymour conjecture
sources:
  - wikipedia: en:50765752@r1320301793
    locator: Kelmans–Seymour conjecture
    note: adopted
    mention: wikipedia://en/50765752
    sections: [Statement]
same_as:
  wikidata: Q24687039
  wikipedia: Kelmans–Seymour conjecture
inventory: [31DF1V2E4S]
---

## Statement

In 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.