Removing Even Crossings - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Removing Even Crossings

Résumé

An edge in a drawing of a graph is called $\textit{even}$ if it intersects every other edge of the graph an even number of times. Pach and Tóth proved that a graph can always be redrawn such that its even edges are not involved in any intersections. We give a new, and significantly simpler, proof of a slightly stronger statement. We show two applications of this strengthened result: an easy proof of a theorem of Hanani and Tutte (not using Kuratowski's theorem), and the result that the odd crossing number of a graph equals the crossing number of the graph for values of at most $3$. We begin with a disarmingly simple proof of a weak (but standard) version of the theorem by Hanani and Tutte.
Fichier principal
Vignette du fichier
dmAE0121.pdf (140.99 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01184387 , version 1 (14-08-2015)

Identifiants

Citer

Michael J. Pelsmajer, Marcus Schaefer, Daniel Štefankovič. Removing Even Crossings. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.105-110, ⟨10.46298/dmtcs.3430⟩. ⟨hal-01184387⟩

Collections

TDS-MACS
36 Consultations
624 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More