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Page 6602 of Mathematical Reviews Vol. , Issue 97K
[page]

1997
*
Mathematical Reviews
*

Summary: “If X is a set

*of*19 vertices*of*a 3-connected cubic*graph*, then either every 12-subset*of*X is*cyclable*or some 17- subset*of*X is*cyclable*.” 97k:05124 05C38 Brandt, Stephan (D-FUB; Berlin) Cycles ... We define a*graph*to be /-*claw*-free if it contains no induced subgraph isomorphic to a A-*claw*. ...##
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Page 65 of Mathematical Reviews Vol. , Issue 97A
[page]

1997
*
Mathematical Reviews
*

1-R1; Orsay);
Li, Hao |Li, Hao'| (F-PARIS11-RI; Orsay);
Liu, Yiping (PRC-NANT; Nanjing);
Tian, Feng (PRC-ASBJ-S; Beijing);
Wu, Zhengsheng (PRC-NANT; Nanjing)

*Sequences*,*claws**and**cyclability**of**graphs*. ... The*graph*G is S-*cyclable*if there is a cycle*of*G containing all vertices*of*S,*and*is S-connectable if for each pair*of*vertices x*and*y*of*G, there is a path joining x*and*...##
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The Parameterized Complexity of Graph Cyclability
[chapter]

2014
*
Lecture Notes in Computer Science
*

The algorithmic version

doi:10.1007/978-3-662-44777-2_41
fatcat:gvppwhyex5dx5ek37o3nsx22ea
*of*the problem, given a*graph*G*and*a non-negative integer k, decide whether the*cyclability**of*G is at least k, is NP-hard. ... The*cyclability**of*a*graph*is the maximum integer k for which every k vertices lie on a cycle. ... For example, every 3-connected*claw*-free*graph*has*cyclability*at least 6 [26]*and*every 3-connected cubic planar*graph*has*cyclability*at least 23 [3] . ...##
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The Parameterized Complexity of Graph Cyclability

2017
*
SIAM Journal on Discrete Mathematics
*

The algorithmic version

doi:10.1137/141000014
fatcat:vr5valgfkbhebbtqbh4vmumyje
*of*the problem, given a*graph*G*and*a non-negative integer k, decide whether the*cyclability**of*G is at least k, is NP-hard. ... The*cyclability**of*a*graph*is the maximum integer k for which every k vertices lie on a cycle. ... For example, every 3-connected*claw*-free*graph*has*cyclability*at least 6 [26]*and*every 3-connected cubic planar*graph*has*cyclability*at least 23 [3] . ...##
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Advances on the Hamiltonian Problem - A Survey

2003
*
Graphs and Combinatorics
*

For completeness

doi:10.1007/s00373-002-0492-x
fatcat:7isvoy4l6jfxxmeftkdcwoyhoy
*of*the presentation*of*both particular questions*and*the general area, it also contains material on closely related topics such as traceable, pancyclic*and*hamiltonian-connected*graphs*...*and*digraphs. ... Theorem 29 Let G be a 2-connected*graph**of*order n*and*S a subset*of*V (G). If σ 2 (S, G) ≥ n, then S is*cyclable*in G. ...##
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The Parameterized Complexity of Graph Cyclability
[article]

2016
*
arXiv
*
pre-print

The algorithmic version

arXiv:1412.3955v2
fatcat:lnn5zibtgvhl7bnu4sx4pt6u2y
*of*the problem, given a*graph*G*and*a non-negative integer k, decide whether the*cyclability**of*G is at least k, is NP-hard. ... The*cyclability**of*a*graph*is the maximum integer k for which every k vertices lie on a cycle. ... For example, every 3-connected*claw*-free*graph*has*cyclability*at least 6 [30]*and*every 3-connected cubic planar*graph*has*cyclability*at least 23 [3] . ...##
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On some intriguing problems in hamiltonian graph theory—a survey

2002
*
Discrete Mathematics
*

We survey results

doi:10.1016/s0012-365x(01)00325-9
fatcat:wcggfjuntbgrjmegqldzdz55hy
*and*open problems in hamiltonian*graph*theory centered around three themes: regular*graphs*, t-tough*graphs*,*and**claw*-free*graphs*. ... A*graph*G is k-*cyclable*if every set*of*k vertices*of*G is contained in a cycle*of*G. [45] ). Every 3-connected*claw*-free*graph*is 9-*cyclable*. ... The equivalences between (1)*and*(2)*of*Theorem 4.9*and**of*Theorem 4.10 appear also in a*sequence**of*equivalences in [50] . ...##
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Cycles in graphs and related problems

2008
*
Dissertationes Mathematicae
*

[84] investigated

doi:10.4064/dm454-0-1
fatcat:nm4dk2d2xzdhvnhjt7t63uk6hu
*cyclability**of**graphs*which are locally*claw*-free*and*satisfy the σ 3 -condition. Theorem 5.16. ... Let G be a 2-connected*graph**of*order n ≥ 33*and*let ∅ = X ⊂ V (G). If (i) no vertex in X ∪ N (X) is a*claw*center; (ii) δ(X) ≥ (n − 2)/3, then X is*cyclable*in G. ... Assume without loss*of*generality that a < f < b < g*and*denote by F the*graph*induced by 0, a, a + 1, . . . , f, . . . , b, . . . , g−1, g, l (see Figure 12 ). ...##
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Claw-free graphs with complete closure

2001
*
Discrete Mathematics
*

We show several structural properties

doi:10.1016/s0012-365x(00)00451-9
fatcat:q6xvs5b36jgw7ljkwcoa4dgv7m
*of**claw*-free*graphs*with complete closure*and*their clique cutsets*and*, using these results, we prove that every*claw*-free*graph*on n vertices with complete closure ... We study some properties*of*the closure concept in*claw*-free*graphs*that was introduced by the ÿrst author. ... Let G be a*claw*-free*graph**and*let G 0 ; G 1 ; : : : ; G t ; t¿1; be a*sequence**of**graphs*such that G 0 = G*and*G i = (G i−1 ) xi−1 for some x i−1 ∈ V EL (G i−1 ); i = 1; : : : ; t. ...##
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Recent Advances on the Hamiltonian Problem: Survey III

2013
*
Graphs and Combinatorics
*

For completeness

doi:10.1007/s00373-013-1377-x
fatcat:mysq2guixrcblm2haaqfu24t6u
*of*the presentation*of*both particular questions*and*the general area, it also contains some material on closely related topics such as traceable, pancyclic*and*Hamiltonian connected*graphs*... Theorem 131 [19] Let b ≤ 3/2*and*let G be a 2-connected*graph*on n ≥ 3 vertices such that bind(G) ≥ b*and*δ(G) ≥ 2−b 3−b n. Then G is pancyclic. ... An almost*claw*-free*graph*G has the centers*of*all*claws*as an independent set*and*the neighborhoods*of*each*of*the centers*of*each*claw*contain 2 vertices adjacent to other neighbors*of*that center. ...##
###
Master index to volumes

2004
*
Discrete Applied Mathematics
*

., The insulation

doi:10.1016/s0166-218x(04)00153-2
fatcat:hajmihwearej7a54evufl2trsi
*sequence**of*a*graph*134 (2004) 77-90 Grinchuk, M.I.*and*V.V. ... Zang, f-Factors in bipartite ðmf Þ-*graphs*Liu, H., Mei Lu*and*F. Tian, Neighborhood unions*and**cyclability**of**graphs*Lodi, E., see P. Flocchini 137 (2004) 197-213 Lohou, C.*and*G. ...##
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Index

2000
*
Discrete Mathematics
*

Skordev, Schur congruences, Carlitz

doi:10.1016/s0012-365x(00)00198-9
fatcat:pvoli2nzdrc6fjmljo5e2gmmky
*sequences**of*polynomials*and*automaticity 214 (2000) 21} 49 Alzer, H.*and*S. ... Schroeder, The congestion*of*n-cube layout on a rectangular grid 213 (2000) 13} 19 Bielak, H., Su$cient condition for Hamiltonicity*of*N -locally connected*claw*-free*graphs*213 (2000) 21} 24 ...##
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Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

2011
*
Journal of combinatorial theory. Series B (Print)
*

Results

doi:10.1016/j.jctb.2011.02.009
fatcat:cvfcg7aaefgo5nxuotyeidbvii
*of*Jackson,*and*Jackson*and*Wormald, imply that the circumference*of*a 3-connected cubic n-vertex*graph*is Ω(n 0.694 ),*and*the circumference*of*a 3-connected*claw*-free*graph*is Ω(n 0.121 ). ... Our proofs imply polynomial time algorithms for finding large Eulerian subgraphs*of*3-edge-connected*graphs**and*long cycles in 3-connected*claw*-free*graphs*. ...*Cyclability*Let G be a*graph**and*e ∈ E(G) with V (e) = {u, v}. ...##
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On Hypohamiltonian and Almost Hypohamiltonian Graphs

2014
*
Journal of Graph Theory
*

The family

doi:10.1002/jgt.21815
fatcat:mal6l7cfe5fcdbbo5fr6zvajjq
*of*all*graphs*G*of**cyclability*|V (G)| coincides with the family*of*all hamiltonian*graphs*,*and**cyclability*|V (G)| − 1 simply means hypohamiltonicity. ... (See also*sequence*A141150 in Sloane's On-Line Encyclopedia*of*Integer*Sequences*[117].) ...##
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Page 159 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

., 97f:05106
Faudree, Raiph J. see Burris, Anita, 971:05075
05C

*Graph*theory 05C38 Favaron, Odile (with Flandrin, Evelyne; Li, Hao'; Liu, Yiping; Tian, Feng'; Wu, Zhengsheng)*Sequences*,*claws**and**cyclability*... (English summary) 97e:05122 — (with Wang, Hairong) Primitive*graphs**and**cyclability**of*cubic*graphs*. ...
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