Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-16T08:28:05.386Z Has data issue: false hasContentIssue false

On the Number of Simple Cycles in Planar Graphs

Published online by Cambridge University Press:  01 September 1999

HELMUT ALT
Affiliation:
Institut für Informatik, Freie Universität Berlin, Takustr. 9, D-14195 Berlin, Germany (e-mail: alt@inf.fu-berlin.de kriegel@inf.fu-berlin.de) http://www.inf.fu-berlin.de/inst/ag-ti
KLAUS KRIEGEL
Affiliation:
Institut für Informatik, Freie Universität Berlin, Takustr. 9, D-14195 Berlin, Germany (e-mail: alt@inf.fu-berlin.de kriegel@inf.fu-berlin.de) http://www.inf.fu-berlin.de/inst/ag-ti

Abstract

Let C(G) denote the number of simple cycles of a graph G and let C(n) be the maximum of C(G) over all planar graphs with n nodes. We present a lower bound on C(n), constructing graphs with at least 2.28n cycles. Applying some probabilistic arguments we prove an upper bound of 3.37n.

We also discuss this question restricted to the subclasses of grid graphs, bipartite graphs, and 3-colourable triangulated graphs.

Type
Research Article
Copyright
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)