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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
On Claw Free Families
 IEICE Trans
, 1994
"... This paper points out that there are two types of claw free families with respect to a level of claw freeness. We formulate them as weak claw free families and strong claw free families. Then, we present sufficient conditions for each type of claw free families. (A similar result is known for weak c ..."
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Cited by 3 (0 self)
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claw free families.) They are represented as some algebraic forms of one way functions. A new example of strong claw free families is also given. 1 Introduction Two permutations f 0 and f 1 are said to be claw free if it is hard to find a pair (x; y) such that f 0 (x) = f 1 (y). [1] showed a digital
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
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
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.
Paireddomination in generalized clawfree graphs
, 2006
"... In this paper, we continue the study of paireddomination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199–206). A set S of vertices in a graph G is a paireddominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect ..."
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Cited by 2 (0 self)
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matching. The paireddomination number of G, denoted by γpr(G), is the minimum cardinality of a paireddominating set of G. If G does not contain a graph F as an induced subgraph, then G is said to be Ffree. Haynes and Slater (Networks 32 (1998) 199–206) showed that if G is a connected graph of order n
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
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
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.
Results 1  10
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