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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 ..."
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Cited by 9 (0 self)
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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
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 ..."
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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
ON EDGECONNECTIVITY OF INSERTED GRAPHS
"... Abstract. The aim of this paper is to estimate the edgeconnectivity of the inserted graph with the help of the degree of vertices of the inserted graph and the edgeconnectivity of the original graph. 1. ..."
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Abstract. The aim of this paper is to estimate the edgeconnectivity of the inserted graph with the help of the degree of vertices of the inserted graph and the edgeconnectivity of the original graph. 1.
Certifying 3EdgeConnectivity
"... Abstract. We present a lineartime certifying algorithm that tests graphs for 3edgeconnectivity. If the input graph G is not 3edgeconnected, the algorithm returns a 2edgecut. If G is 3edgeconnected, the algorithm returns a construction sequence that constructs G from the graph with two nodes ..."
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Abstract. We present a lineartime certifying algorithm that tests graphs for 3edgeconnectivity. If the input graph G is not 3edgeconnected, the algorithm returns a 2edgecut. If G is 3edgeconnected, the algorithm returns a construction sequence that constructs G from the graph with two
On Bicritical Snarks
 Math. Slovaca
, 1997
"... Bicritical snarks are the irreducible ones with respect to the reductions considered by Nedela and Skoviera in [7]. We give a natural characterization of bicritical snarks and we characterize the elementary extensions of a snark. This solves Problem No. 6 of [7], and yields a method to construct al ..."
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Cited by 3 (2 self)
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Bicritical snarks are the irreducible ones with respect to the reductions considered by Nedela and Skoviera in [7]. We give a natural characterization of bicritical snarks and we characterize the elementary extensions of a snark. This solves Problem No. 6 of [7], and yields a method to construct
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Edgeconnectivity augmentations of graphs and hypergraphs
"... A. Frank (Augmenting graphs to meet edgeconnectivity requirements, ..."
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Cited by 3 (2 self)
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A. Frank (Augmenting graphs to meet edgeconnectivity requirements,
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
AN n 5/2 ALGORITHM FOR MAXIMUM MATCHINGS IN BIPARTITE GRAPHS
, 1973
"... The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. ..."
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Cited by 712 (1 self)
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The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/.
Results 1  10
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923,917