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Generalizations of the Crossing Lemma (2509.14074v1)
Published 17 Sep 2025 in math.CO
Abstract: The crossing number of a graph is the minimum number of crossings over all of its drawings on the plane. The Crossing Lemma, proved more than 40 years ago, is a tight lower bound on the crossing number of a graph in terms of the number of vertices and edges. It is definitely the most important inequality on crossing numbers. We review some generalizations and applications of the Crossing Lemma.
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