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Minimal ClawFree Graphs
, 2007
"... A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and character ..."
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A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices
Hamiltonian clawfree graphs
, 2005
"... A graph is clawfree if it does not have an induced subgraph isomorphic to a K1,3. In this paper, we proved the every 3connected, essentially 11connected clawfree graph is hamiltonian. We also present two related results concerning hamiltonian clawfree graphs. 1 ..."
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A graph is clawfree if it does not have an induced subgraph isomorphic to a K1,3. In this paper, we proved the every 3connected, essentially 11connected clawfree graph is hamiltonian. We also present two related results concerning hamiltonian clawfree graphs. 1
Pancyclicity in Clawfree Graphs
"... In this paper, we present several conditions for K1,3free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1,3free graph with minimum degree sum δ2> 2 3n+ 1 − 4; every {K1,3, P7}free graph with δ2 ≥ 9; every {K1,3, Z4}free graph with δ2 ≥ 9; and every K1,3 ..."
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,3free graph with maximum degree ∆, diam(G) < ∆+64 and δ2 ≥ 9 is subpancyclic. Key words: clawfree, pancyclicity, forbidden subgraphs 1
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 ..."
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Cited by 12 (1 self)
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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
INDEPENDENCE COMPLEXES OF CLAWFREE GRAPHS
, 2005
"... We study the class of independence complexes of clawfree graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a clawfree graph with ..."
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Cited by 18 (6 self)
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We study the class of independence complexes of clawfree graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a clawfree graph
Quadrangularly connected clawfree graphs
"... A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree gr ..."
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Cited by 1 (1 self)
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A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of lcycles (3 ≤ l ≤ 4) C1, C2,..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) � = ∅ for i = 1, 2,..., r − 1. In this paper, we show that every quadrangularly connected clawfree
Strengthening the Closure Concept in ClawFree Graphs
, 1999
"... We give a strengthening of the closure concept for clawfree graphs introduced by the second author in 1997. The new closure of a clawfree graph G defined here is uniquely determined and preserves the value of the circumference of G. We present an infinite family of graphs with n vertices and 3 2 ..."
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Cited by 79 (15 self)
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We give a strengthening of the closure concept for clawfree graphs introduced by the second author in 1997. The new closure of a clawfree graph G defined here is uniquely determined and preserves the value of the circumference of G. We present an infinite family of graphs with n vertices and 3 2
Clawfree circularperfect graphs
 EUROCOMB07 EUROPEAN CONFERENCE ON COMBINATORICS, GRAPH THEORY AND APPLICATIONS, ESPAGNE
, 2007
"... The circular chromatic number of a graph is a wellstudied refinement of the chromatic number. Circularperfect graphs is a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies clawfree circularperfect graphs. A consequence of the strong perfect g ..."
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Cited by 12 (2 self)
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graph theorem is that minimal circularimperfect graphs G have min{α(G), ω(G)} = 2. In contrast to this result, it is shown in [9] that minimal circularimperfect graphs G can have arbitrarily large independence number and arbitrarily large clique number. We prove that clawfree minimal circular
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. ..."
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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.
ClawFree Graphs With Complete Closure
, 1999
"... We study some properties of the closure concept in clawfree graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite classes of nonpancyclic graphs with pancyclic closure. We show several ..."
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Cited by 1 (0 self)
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We study some properties of the closure concept in clawfree graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite classes of nonpancyclic graphs with pancyclic closure. We show several
Results 1  10
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5,363