Loading...
research article
Thrackles: An improved upper bound
April 30, 2019
A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is 3/2(n-1), and that this bound is best possible for infinitely many values of n. (C) 2019 Published by Elsevier B.V.
Type
research article
Web of Science ID
WOS:000466061100020
Authors
Publication date
2019-04-30
Publisher
Published in
Volume
259
Start page
226
End page
231
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
June 18, 2019
Use this identifier to reference this record