BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//jEvents 2.0 for Joomla//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VTIMEZONE
TZID:Europe/Budapest
END:VTIMEZONE
BEGIN:VEVENT
UID:4i3hs5od7nc0fvh85o4dmavl51@google.com
CATEGORIES:{lang hu}Kombinatorika szeminárium{/lang}{lang en}Combinatorics seminar{/lang}
SUMMARY:Éva Czabarka (University of South Carolina): Midrange crossing constants for graphs classes
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:
Abstract.
For positive integers $n$ and $e$, let $\kappa(n,e)$ be
the minimum crossing number (the standard planar crossing number) taken ove
r all graphs with $n$ vertices and at least $e$ edges. Pach, Spencer and Tó
th [Discrete and Computational Geometry{\bf 24} 623--644, (2000)] showed th
at $\kappa(n,e) n^2/e^3$ tends to a positive constant (called midrange cros
sing constant) as $n\to \infty$ and $n << e << n^2$, proving a conjecture o
f Erdős and Guy. In this note, we extend their proof to show that the midra
nge crossing constant exists for graph classes that satisfy a certain set o
f graph properties. As a corollary, we show that the the midrange crossing
constant exists for the family of bipartite graphs. All these results have
their analogues for rectilinear crossing numbers.
This is joint work wi
th Josiah Reiswig, Lászlo Székely and Zhiyu Wang.
DTSTAMP:20240328T220558Z
DTSTART;TZID=Europe/Budapest:20190513T160000
DTEND;TZID=Europe/Budapest:20190513T170000
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR