The Kelmans-Seymour conjecture for apex graphs
Abstract
We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided K_5 or a K-_4 (= K_4 with a single edge removed) as a subgraph. Together with a recent result of Ma and Yu that every nonplanar 5-connected graph containing K-_4 as a subgraph has a subdivided K_5; this settles the Kelmans-Seymour conjecture for apex graphs.
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