Abstract
An edge e of a graph G is said to be crossing-critical if cr( G − e) < cr( G), where cr( G) denotes the crossing number of G on the plane. It is proved that any crossing-critical edge e of a graph G for which cr( G − e) ≤ 1 belongs to a subdivision of K 5 or K 3, 3, the Kuratowski subgraphs of G. Further, as regards crossing-critical edges e of G for which cr( G − e) ≥ 5, it is shown that the properties of “being a crossing-critical edge of G” and “being contained in a Kuratowski subgraph of G” are independent.
Published Version
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