Results 1  10
of
31,966
A Generalization of FanType Conditions for Hamiltonian and HamiltonianConnected Graphs
, 1993
"... In this paper, we prove if G is a 2conneded graph of order n and roa.x{d(u), d(v)};?:: j for each pair of nonadjacent vertices u, v of G wi.th 1::; IN (u) n N (v) I s Ct 2, then either G is Hamiltonian or else G belongs to one of a family of exceptional graphs. We give a similar sufficient conditi ..."
New Sufficient Conditions for sHamiltonian Graphs and sHamiltonian Connected Graphs
"... Abstract: A graph G is sHamiltonian if for any S ⊆ V (G) of order at most s, G − S has a Hamiltoniancycle, and sHamiltonian connected if for any S ⊆ V (G) of order at most s, G − S is Hamiltonianconnected. Let k> 0, s ≥ 0 be two integers. The following are proved in this paper: (1) Let k ≥ s ..."
Abstract
 Add to MetaCart
Abstract: A graph G is sHamiltonian if for any S ⊆ V (G) of order at most s, G − S has a Hamiltoniancycle, and sHamiltonian connected if for any S ⊆ V (G) of order at most s, G − S is Hamiltonianconnected. Let k> 0, s ≥ 0 be two integers. The following are proved in this paper: (1) Let k
Discrete Applied Mathematics 100 (2000) 145–153 PseudoHamiltonianconnected graphs
, 1999
"... ..."
Hamiltonianconnected graphs
, 2008
"... For a simple graph G, let NC D(G) = min{N(u) ∪ N(v)  + d(w) : u, v, w ∈ V (G), uv ∈ E(G), wv or wu ∈ E(G)}. In this paper, we prove that if NC D(G) ≥ V (G), then either G is Hamiltonianconnected, or G belongs to a wellcharacterized class of graphs. The former results by Dirac, Ore and Fau ..."
Abstract
 Add to MetaCart
For a simple graph G, let NC D(G) = min{N(u) ∪ N(v)  + d(w) : u, v, w ∈ V (G), uv ∈ E(G), wv or wu ∈ E(G)}. In this paper, we prove that if NC D(G) ≥ V (G), then either G is Hamiltonianconnected, or G belongs to a wellcharacterized class of graphs. The former results by Dirac, Ore
Advances on the Hamiltonian problem  A survey
, 2002
"... This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs. ..."
Abstract

Cited by 34 (0 self)
 Add to MetaCart
This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonianconnected graphs and digraphs.
On shamiltonianconnected line graphs
, 2007
"... A graph G is hamiltonianconnected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is shamiltonianconnected if the deletion of any vertex subset with at most s vertices results in a hamiltonianconnected graph. In this paper, we prove that th ..."
Abstract
 Add to MetaCart
A graph G is hamiltonianconnected if any two of its vertices are connected by a Hamilton path (a path including every vertex of G); and G is shamiltonianconnected if the deletion of any vertex subset with at most s vertices results in a hamiltonianconnected graph. In this paper, we prove
Closure and HamiltonianConnectivity of ClawFree Graphs
 Discrete Math
, 1999
"... In [3], the closure cl(G) for a clawfree graph G is defined, and it is proved that G is hamiltonian if and only if cl(G) is hamiltonian. On the other hand, there exist infinitely many clawfree graphs G such that G is not hamiltonianconnected (resp. homogeneously traceable) while cl(G) is hamilton ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
In [3], the closure cl(G) for a clawfree graph G is defined, and it is proved that G is hamiltonian if and only if cl(G) is hamiltonian. On the other hand, there exist infinitely many clawfree graphs G such that G is not hamiltonianconnected (resp. homogeneously traceable) while cl
HamiltonianConnectivity and Related Property on Folded Hypercubes
"... Abstract — In this paper, we analysis a hypercubelike structure, called the Folded Hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the ndimensional folded hypercube is bipartite when n is odd. We also show that the ndimens ..."
Abstract
 Add to MetaCart
dimensional folded hypercube is strongly Hamiltonianlaceable when n is odd, and is Hamiltonianconnected when n = 1 or n( ≥ 2) is even. Keywords: Folded hypercubes, Hamiltonianconnectivity, strongly Hamiltonianlaceability, bipartite graphs.
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 ..."
Abstract

Cited by 801 (1 self)
 Add to MetaCart
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
Weekly hamiltonianconnected ordinary multipartite tournaments
 Discrete Math
, 1995
"... We characterize weakly Hamiltonianconnected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite tourn ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
We characterize weakly Hamiltonianconnected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite
Results 1  10
of
31,966