id: 05763167
dt: a
an: 05763167
au: Pelsmajer, Michael J.; Schaefer, Marcus; štefankovič, Daniel
ti: Removing even crossings.
so: Felsner, Stefan (ed.), 2005 European conference on combinatorics, graph
    theory and applications (EuroComb ’05). Extended abstracts from the
    conference, Technische Universität Berlin, Berlin, Germany, September
    5‒9, 2005. Paris: Maison de l’Informatique et des Mathématiques
    Discrètes (MIMD). Discrete Mathematics \& Theoretical Computer
    Science. Proceedings. AE, 105-110, electronic only (2005).
py: 2005
pu: Paris: Maison de l’Informatique et des Mathématiques Discrètes (MIMD)
la: EN
cc: 
ut: Hanani’s theorem; Tutte’s theorem; even crossings; crossing number; odd
    crossing number; independent odd crossing number
ci: 
li: http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAE0121
ab: Summary: An edge in a drawing of a graph is called 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.
rv: