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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.  ... 

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  ... 

The Parameterized Complexity of Graph Cyclability [chapter]

Petr A. Golovach, Marcin Kamiński, Spyridon Maniatis, Dimitrios M. Thilikos
2014 Lecture Notes in Computer Science  
The algorithmic version 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] .  ... 
doi:10.1007/978-3-662-44777-2_41 fatcat:gvppwhyex5dx5ek37o3nsx22ea

The Parameterized Complexity of Graph Cyclability

Petr A. Golovach, Marcin Kamiński, Spyridon Maniatis, Dimitrios M. Thilikos
2017 SIAM Journal on Discrete Mathematics  
The algorithmic version 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] .  ... 
doi:10.1137/141000014 fatcat:vr5valgfkbhebbtqbh4vmumyje

Advances on the Hamiltonian Problem - A Survey

Ronald J. Gould
2003 Graphs and Combinatorics  
For completeness 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.  ... 
doi:10.1007/s00373-002-0492-x fatcat:7isvoy4l6jfxxmeftkdcwoyhoy

The Parameterized Complexity of Graph Cyclability [article]

Petr A. Golovach, Marcin Kamiński, Spyridon Maniatis, Dimitrios M. Thilikos
2016 arXiv   pre-print
The algorithmic version 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] .  ... 
arXiv:1412.3955v2 fatcat:lnn5zibtgvhl7bnu4sx4pt6u2y

On some intriguing problems in hamiltonian graph theory—a survey

H.J. Broersma
2002 Discrete Mathematics  
We survey results 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] .  ... 
doi:10.1016/s0012-365x(01)00325-9 fatcat:wcggfjuntbgrjmegqldzdz55hy

Cycles in graphs and related problems

Antoni Marczyk
2008 Dissertationes Mathematicae  
[84] investigated 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 ).  ... 
doi:10.4064/dm454-0-1 fatcat:nm4dk2d2xzdhvnhjt7t63uk6hu

Claw-free graphs with complete closure

Zdeněk Ryjáček, Akira Saito, R.H Schelp
2001 Discrete Mathematics  
We show several structural properties 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.  ... 
doi:10.1016/s0012-365x(00)00451-9 fatcat:q6xvs5b36jgw7ljkwcoa4dgv7m

Recent Advances on the Hamiltonian Problem: Survey III

Ronald J. Gould
2013 Graphs and Combinatorics  
For completeness 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.  ... 
doi:10.1007/s00373-013-1377-x fatcat:mysq2guixrcblm2haaqfu24t6u

Master index to volumes

2004 Discrete Applied Mathematics  
., The insulation 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.  ... 
doi:10.1016/s0166-218x(04)00153-2 fatcat:hajmihwearej7a54evufl2trsi

Index

2000 Discrete Mathematics  
Skordev, Schur congruences, Carlitz 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  ... 
doi:10.1016/s0012-365x(00)00198-9 fatcat:pvoli2nzdrc6fjmljo5e2gmmky

Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

Mark Bilinski, Bill Jackson, Jie Ma, Xingxing Yu
2011 Journal of combinatorial theory. Series B (Print)  
Results 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}.  ... 
doi:10.1016/j.jctb.2011.02.009 fatcat:cvfcg7aaefgo5nxuotyeidbvii

On Hypohamiltonian and Almost Hypohamiltonian Graphs

Carol T. Zamfirescu
2014 Journal of Graph Theory  
The family 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].)  ... 
doi:10.1002/jgt.21815 fatcat:mal6l7cfe5fcdbbo5fr6zvajjq

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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