Results 1 
8 of
8
ON CYCLIC EDGECONNECTIVITY OF FULLERENES
, 2007
"... A graph is said to be cyclic kedgeconnected, 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 cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components ind ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
A graph is said to be cyclic kedgeconnected, 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 cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components induces a single kcycle. It is known that fullerenes, that is, 3connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclic 5edgeconnected. In this article it is shown that a fullerene F containing a nontrivial cyclic5edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is n ⌊ shown that F has a Hamilton cycle, and as a consequence at least 15 ·2 20 ⌋ perfect matchings, where n is the order of F.
CONTENTS CONTENTS
, 2010
"... In this paper we present the maximum flow algorithm in O(n log n) for directed planar graphs of Glencore Borradail and Philip Klein published in 2009 in [1]. Further we are going to present and analyse an implementation of this algorithm. To analyse the maximum flow algorithm we also use an algorith ..."
Abstract
 Add to MetaCart
In this paper we present the maximum flow algorithm in O(n log n) for directed planar graphs of Glencore Borradail and Philip Klein published in 2009 in [1]. Further we are going to present and analyse an implementation of this algorithm. To analyse the maximum flow algorithm we also use an algorithm to find the maximal running time of a an algorithm for planar graphs which is based on transforming maximal planar graphs to other maximal planar graphs by Lawson flips. This algorithm will be presented and analyzed as well.
ON CYCLIC EDGECONNECTIVITY OF FULLERENES
, 2007
"... A graph is said to be cyclic kedgeconnected, 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 cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components ind ..."
Abstract
 Add to MetaCart
A graph is said to be cyclic kedgeconnected, 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 cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components induces a single kcycle. It is known that fullerenes, that is, 3connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclic 5edgeconnected. In this article it is shown that a fullerene F containing a nontrivial cyclic5edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is n ⌊ shown that F has a Hamilton cycle, and as a consequence at least 15 ·2 20 ⌋ perfect matchings, where n is the order of F.
CONTENTS
"... In this paper we present the maximum flow algorithm in O(n log n) for directed planar graphs of Glencore Borradail and Philip Klein published in 2009 in [1]. Further we are going to present and analyse an implementation of this algorithm. To analyse the maximum flow algorithm we also use an algorith ..."
Abstract
 Add to MetaCart
In this paper we present the maximum flow algorithm in O(n log n) for directed planar graphs of Glencore Borradail and Philip Klein published in 2009 in [1]. Further we are going to present and analyse an implementation of this algorithm. To analyse the maximum flow algorithm we also use an algorithm to find the maximal running time of a an algorithm for planar graphs which is based on transforming maximal planar graphs to other maximal planar graphs by Lawson flips.
Recursive generation of simple planar 5regular graphs and pentangulations
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2011
"... ..."
(Show Context)
Coxeter groups, hyperbolic cubes, and acute triangulations
, 2014
"... Let C(L) be the rightangled Coxeter group defined by an abstract triangulation L of S2. We show that C(L) is isomorphic to a hyperbolic rightangled reflection group if triangulation of S2 can be realized as an acute triangulation exactly when it satisfies a combinatorial condition called “flag no ..."
Abstract
 Add to MetaCart
(Show Context)
Let C(L) be the rightangled Coxeter group defined by an abstract triangulation L of S2. We show that C(L) is isomorphic to a hyperbolic rightangled reflection group if triangulation of S2 can be realized as an acute triangulation exactly when it satisfies a combinatorial condition called “flag nosquare”. We also study generalizations of this result to other angle bounds, other planar surfaces and other dimensions. 1
Construction of planar 4connected triangulations
, 2014
"... In this article we describe a recursive structure for the class of 4connected triangulations or – equivalently – cyclically 4connected plane cubic graphs. ..."
Abstract
 Add to MetaCart
(Show Context)
In this article we describe a recursive structure for the class of 4connected triangulations or – equivalently – cyclically 4connected plane cubic graphs.