Results 1  10
of
3,059
ON HAMILTONICITY OF {CLAW, NET}FREE GRAPHS
, 2006
"... An stpath is a path with the endvertices s and t. An spath is a path with an endvertex s. The results of this paper include necessary and sufficient conditions for a {claw, net}free graph G with s,t ∈ V (G) and e ∈ E(G) to have (1) a Hamiltonian spath, (2) a Hamiltonian stpath, (3) a Hamilton ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Hamiltonian s and stpaths containing e when G has connectivity one, and (4) a Hamiltonian cycle containing e when G is 2connected. These results imply that a connected {claw, net}free graph has a Hamiltonian path and a 2connected {claw, net}free graph has a Hamiltonian cycle [3]. Our proofs of (1
Claw and Netfree Graphs
, 2009
"... quirements for an advanced degree from Emory University, I hereby grant to Emory University and its agents the nonexclusive license to archive, make accessible, and display my thesis or dissertation in whole or in part in all forms of media, now or hereafter known, including display on the world wi ..."
Abstract
 Add to MetaCart
quirements for an advanced degree from Emory University, I hereby grant to Emory University and its agents the nonexclusive license to archive, make accessible, and display my thesis or dissertation in whole or in part in all forms of media, now or hereafter known, including display on the world wide web. I understand that I may select some access restrictions as part of the online submission of this thesis or dissertation. I retain all ownership rights to the copyright of the thesis or dissertation. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. Signature:
On Linear and Circular Structure of (claw, net)Free Graphs
, 2003
"... We prove that every (claw, net)free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present alS[SE timealen##ES which, for a given (claw, net)free graph, finds either a dominating pair or an induceddoubl dominatingcycln We show aln how one can uses ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We prove that every (claw, net)free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present alS[SE timealen##ES which, for a given (claw, net)free graph, finds either a dominating pair or an induceddoubl dominatingcycln We show aln how one can
Forbidden Subgraphs, Hamiltonicity and Closure in ClawFree Graphs
 Discrete Math
, 1999
"... We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2connected clawfree and P 7 free, or clawfree and Z 4  free, or clawfree and eiffelfree graph is ei ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2connected clawfree and P 7 free, or clawfree and Z 4  free, or clawfree and eiffelfree graph
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden
A Note on Hamiltonicity of Generalized NetFree Graphs of Large Diameter
"... A generalized (i; j; k)net N i;j;k is the graph obtained by identifying each of the vertices of a triangle with an endvertex of one of three vertexdisjoint paths of lengths i; j; k. We prove that every 2connected clawfree N 1;2;j free graph of diameter at least maxf7; 2jg (j 2) is hamiltonian ..."
Abstract
 Add to MetaCart
A generalized (i; j; k)net N i;j;k is the graph obtained by identifying each of the vertices of a triangle with an endvertex of one of three vertexdisjoint paths of lengths i; j; k. We prove that every 2connected clawfree N 1;2;j free graph of diameter at least maxf7; 2jg (j 2
CRITICAL GRAPHS FOR SUBPANCYCLICITY OF 3CONNECTED CLAWFREE GRAPHS
"... Abstract. Let Fk be the family of graphs G such that all sufficiently large kconnected clawfree graphs which contain no induced copies of G are subpancyclic. We show that for every k ≥ 3 the family Fk is infinite and make the first step towards the complete characterization of the family F3. 1. ..."
Abstract
 Add to MetaCart
Abstract. Let Fk be the family of graphs G such that all sufficiently large kconnected clawfree graphs which contain no induced copies of G are subpancyclic. We show that for every k ≥ 3 the family Fk is infinite and make the first step towards the complete characterization of the family F3. 1.
TRACEABILITY IN SMALL CLAWFREE GRAPHS
"... Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1. ..."
Abstract
 Add to MetaCart
Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1.
Results 1  10
of
3,059