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On ffactors in clawfree graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 52 (2012), PAGES 133–140
, 2012
"... Let G be a 2connected clawfree graph such that δ(G) ≥ 5. Then for every function f: V (G) →{1, 2}, where ∑ x∈V (G) f(x) is even, G has an ffactor. ..."
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Let G be a 2connected clawfree graph such that δ(G) ≥ 5. Then for every function f: V (G) →{1, 2}, where ∑ x∈V (G) f(x) is even, G has an ffactor.
On Factors of 4Connected ClawFree Graphs
 J. GRAPH THEORY
, 1999
"... We consider the existence of several different kinds of factors in 4connected clawfree graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4connected line graph is hamiltonian, i.e. has ..."
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Cited by 12 (3 self)
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We consider the existence of several different kinds of factors in 4connected clawfree graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4connected line graph is hamiltonian, i.e. has
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
Clique minors in clawfree graphs
 J. Combin. Theory Ser. B
"... Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n α. In this paper we prove that this ..."
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Cited by 1 (0 self)
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that this is true for connected clawfree graphs with α ≥ 3. We also show that this result is tight by providing an infinite family of clawfree graphs with α ≥ 3 that do not have a clique minor of size larger than n α
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 ..."
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Cited by 5 (3 self)
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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
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
Closure concept for 2factors in clawfree graphs
, 2010
"... We introduce a closure concept for 2factors in clawfree graphs that generalizes the closure introduced by the first author. The 2factor closure of a graph is uniquely determined and the closure operation turns a clawfree graph into the line graph of a graph containing no cycles of length at most ..."
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Cited by 1 (1 self)
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We introduce a closure concept for 2factors in clawfree graphs that generalizes the closure introduced by the first author. The 2factor closure of a graph is uniquely determined and the closure operation turns a clawfree graph into the line graph of a graph containing no cycles of length
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
PACKING 3VERTEX PATHS IN CLAWFREE GRAPHS
, 711
"... A Λfactor of a graph G is a spanning subgraph of G whose every component is a 3vertex path. Let v(G) be the number of vertices of G. A graph is clawfree if it does not have a subgraph isomorphic to K1,3. Our results include the following. Let G be a 3connected clawfree graph, x ∈ V (G), e = xy ∈ ..."
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A Λfactor of a graph G is a spanning subgraph of G whose every component is a 3vertex path. Let v(G) be the number of vertices of G. A graph is clawfree if it does not have a subgraph isomorphic to K1,3. Our results include the following. Let G be a 3connected clawfree graph, x ∈ V (G), e = xy
Results 1  10
of
2,116,761