The Kelmans–Seymour conjecture is a conjecture in graph theory that relates to the structure of certain types of graphs. Specifically, it deals with the behavior of complete graphs and the existence of specific subgraphs within them. Formulated by Paul Kelmans and Neil Seymour, the conjecture states that every 2-edge-connected graph can be represented as a graph obtained from a complete graph by the contraction of edges.
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