Crossing lemmas for multigraphs?
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Guillem Perarnau [1]
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[1] Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya
Barcelona, España
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- Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 7-7
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
The celebrated Crossing Lemma of Thurston and Ajtai, Chvátal, Newborn, and Szemerédi gives anasymptotically tight lower bound on the number of edge crossing in any drawing of a graph G in theplane which has n vertices and e > 3n − 6 edges. The lemma has found many applications in topologicalgraph theory, additive number theory, combinatorial geometry, and elsewhere. In order to extend itsrange of applications, for more than 40 years, there have been many attempts to strengthen this lemmafor various special classes of graphs, and to generalize it to multigraphs (where there can be severaledges between any pair of vertices). We describe some recent efforts in this direction, and raise severalopen problems.
