PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On cyclic edge-connectivity of fullerenes
Dragan Marušič and Klavdija Kutnar
Discrete appl. math. Volume 156, Number 10, pp. 1661-1669, 2008. ISSN 0166-218X

Abstract

A graph is said to be cyclically k-edge-connected, if at least k edges must be removed to disconnect it into two components, each containing a cycle. Such a set of k edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single k-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene F containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that F has a Hamilton cycle, and as a consequence at least 15·2n/20-1/2 perfect matchings, where n is the order of F.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8214
Deposited By:Boris Horvat
Deposited On:21 February 2012