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45,813
Unifying Results On Hamiltonian ClawFree Graphs
, 1995
"... This work was motivated by many (recent) papers on hamiltonicity of clawfree graphs, i.e. graphs that do not contain K 1;3 as an induced subgraph. By combining ideas from these papers with some new observations, we unify several of the existing sufficiency results, using a new sufficient condition ..."
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consisting of seven subconditions. If each pair of vertices at distance two of a 2connected clawfree graph G satisfies at least one of these subconditions, then G is hamiltonian. We also present infinite classes of examples of graphs showing that these subconditions are, in some sense, independent. AMS
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
2Factors in Hamiltonian Graphs
"... We show that every hamiltonian clawfree graph with a vertex x of degree d(x) ≥ 7 has a 2factor consisting of exactly two cycles. 1 ..."
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We show that every hamiltonian clawfree graph with a vertex x of degree d(x) ≥ 7 has a 2factor consisting of exactly two cycles. 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
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
Closure and Stable Hamiltonian Properties in ClawFree Graphs
, 1999
"... In the class of kconnected clawfree graphs, we study the stability of some hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any of these ..."
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In the class of kconnected clawfree graphs, we study the stability of some hamiltonian properties under a closure operation introduced by the third author. We prove that (i) the properties of pancyclicity, vertex pancyclicity and cycle extendability are not stable for any k (i.e., for any
Hamiltonian cycles in 3connected Clawfree graphs
 DISCRETE MATHEMATICS
, 2002
"... It is shown that every 3connected clawfree graph having at most 6 − 7 vertices is hamiltonian, where is the minimum degree. ..."
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It is shown that every 3connected clawfree graph having at most 6 − 7 vertices is hamiltonian, where is the minimum degree.
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
Second Hamiltonian cycles in clawfree graphs
, 2015
"... Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most clawfree Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not cove ..."
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Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most clawfree Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs
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.
Results 1  10
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45,813