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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
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
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
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.
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
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
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 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
Clawfree Graphs VI. Colouring
, 2011
"... In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can be ..."
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Cited by 4 (0 self)
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In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can
Results 1  10
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5,497