Filters








715 Hits in 5.5 sec

9-Connected Claw-Free Graphs Are Hamilton-Connected

Stephan Brandt
1999 Journal of combinatorial theory. Series B (Print)  
claw-free graphs are Hamilton-connected.  ...  The main result of this note verifies the conjecture for k=9. Theorem 3. Every 9-connected claw-free graph is Hamilton-connected.  ... 
doi:10.1006/jctb.1998.1871 fatcat:shaho73nlnha3ghkes3in4ribe

Hamiltonicity in claw-free graphs

F.Bruce Shepherd
1991 Journal of combinatorial theory. Series B (Print)  
We strengthen this result for CN-free graphs of higher connectivity. For example, we show 3-connected CN-free graphs are both Hamilton connected and pancyclic.  ...  A graph is claw-free if it contains no induced subgraph isomorphic to a K"3. This paper studies hamiltonicity in two subclasses of claw-free graphs.  ...  We show that these graphs are Hamilton connected.  ... 
doi:10.1016/0095-8956(91)90074-t fatcat:t6g6t3xbpnfgvhnxmbwxq6zcca

How Many Conjectures Can You Stand? A Survey

H. J. Broersma, Z. Ryjáček, P. Vrána
2011 Graphs and Combinatorics  
We survey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian.  ...  Conjecture 23 Every 4-connected claw-free graph is Hamilton-connected.  ...  Conjecture 25 Every 4-connected claw-free graph is 1-Hamilton-connected.  ... 
doi:10.1007/s00373-011-1090-6 fatcat:jj7oxvyx5vhrzdjtv2qyj7nysy

Closure Concepts: A Survey

Hajo Broersma, Zdeněk Ryjáček, Ingo Schiermeyer
2000 Graphs and Combinatorics  
As a consequence, for any graph G with cl n G K n (and n 3), a Hamilton cycle can be found in polynomial time, whereas this problem is NP-hard for general graphs.  ...  The ®rst and now well-known result of this type was established by Bondy and Chva Âtal in a paper published in 1976: If u and v are two nonadjacent vertices with degree sum n in a graph G on n vertices  ...  Every 9-connected claw-free graph is Hamilton-connected. This result motivates the following question.  ... 
doi:10.1007/s003730050002 fatcat:6qncwca2bvhtvh7oqfvoskidhq

Forbidden triples for hamiltonicity

Jan Brousek
2002 Discrete Mathematics  
In this paper we characterize all triples of connected graphs C; X; Y (where C is a claw) and such that every 2-connected CXY -free graph G is hamiltonian.This result together with a previous result by  ...  Faudree, Gould, Jacobson, and Lesniak give a full characterization of triples of forbidden subgraphs implying hamiltonicity of 2-connected graphs.  ...  The graphs P 3; 3; 3 and P T; T; T are 2-connected, non-hamiltonian and claw-free and thus the set of CXY -free graphs contains neither P 3; 3; 3 nor P T; T; T .  ... 
doi:10.1016/s0012-365x(01)00326-0 fatcat:siajq7tfwvenpgdbsqgeergnai

Extremal problems on the Hamiltonicity of claw-free graphs

Binlong Li, Bo Ning, Xing Peng
2018 Discrete Mathematics  
Similar results for the traceability of connected claw-free graphs are also obtained.  ...  Our tools include Ryjáček's claw-free closure theory and Brousek's characterization of minimal 2-connected claw-free non-Hamiltonian graphs.  ...  We prove the following lemma on Hamiltonicity of closed claw-free graphs. Lemma 1. Let G be a 2-connected closed claw-free graph on n vertices.  ... 
doi:10.1016/j.disc.2018.06.023 fatcat:ywmjhwndlzacnopugbh2gk64qq

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.  ...  Then; the following statements are equivalent: (1) Every k-connected claw-free graph is hamiltonian. (2) Every k-connected claw-free graph has an f(n)-path-factor. (3) Every k-connected claw-free graph  ...  Presently, the best su cient minimum degree condition for hamiltonicity of 3-connected claw-free graphs we are aware of is due to Favaron and Fraisse [31] ; using the claw-free closure and a relationship  ... 
doi:10.1016/s0012-365x(01)00325-9 fatcat:wcggfjuntbgrjmegqldzdz55hy

Forbidden subgraphs, stability and hamiltonicity

Jan Brousek, Zdeněk Ryjáček, Ingo Schiermeyer
1999 Discrete Mathematics  
We characterize all connected graph.,; A such that the class of all CA-free graphs (where C denotes the claw) is stable.  ...  Using this result, we prove that every 2-connected and CHPs-free, CHZs-free or CHNt.l.4-free graph is either hamiltonian or belongs to some classes of exceptional graphs (all of them having" connectivity  ...  Ever), non-Hamilton/an 2-connected claw-free graph contains an induced subyraph F E ,~.  ... 
doi:10.1016/s0012-365x(99)90053-5 fatcat:s7toibwmkbf7to5t6g3ivcmo6e

Forbidden subgraphs, stability and hamiltonicity

J Brousek
1999 Discrete Mathematics  
We characterize all connected graph.,; A such that the class of all CA-free graphs (where C denotes the claw) is stable.  ...  Using this result, we prove that every 2-connected and CHPs-free, CHZs-free or CHNt.l.4-free graph is either hamiltonian or belongs to some classes of exceptional graphs (all of them having" connectivity  ...  Ever), non-Hamilton/an 2-connected claw-free graph contains an induced subyraph F E ,~.  ... 
doi:10.1016/s0012-365x(98)00229-5 fatcat:etu2wmh74randnlzfpveua3frq

Spectral radius and traceability of connected claw-free graphs

Bo Ning, Binlong Li
2016 Filomat  
Let G be a connected claw-free graph on n vertices and G be its complement graph. Let μ(G) be the spectral radius of G.  ...  Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively.  ...  There are examples of 3-connected non-Hamiltonian claw-free (even line) graphs, but it is a long-standing conjecture that all 4-connected claw-free graphs are Hamiltonian (and then, traceable).  ... 
doi:10.2298/fil1609445n fatcat:fhyupk5dxneydivvtepv7dyqa4

Line graphs of multigraphs and Hamilton-connectedness of claw-free graphs

Zdeněk Ryjáček, Petr Vrána
2010 Journal of Graph Theory  
) is equivalent with the statement that every 4-connected claw-free graph is Hamilton-connected.  ...  As an application, we show that every 7-connected claw-free graph is Hamilton-connected, and we show that the wellknown conjecture by Matthews and Sumner (every 4-connected clawfree graph is hamiltonian  ...  claw-free graphs (there The existence of a connectivity bound for Hamilton-connectedness in claw-free graphs was established by Brandt [5] who proved that every 9connected claw-free graph is Hamilton-connected  ... 
doi:10.1002/jgt.20498 fatcat:wehpsrgwebaalezmeqvmuqplpq

On implicit heavy subgraphs and Hamiltonicity of 2-connected graphs

Ligong Wang, Wojciech Wideł, Wei Zheng
2018 Discussiones Mathematicae Graph Theory  
A graph G of order n is implicit claw-heavy if in every induced copy of K 1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n.  ...  Math. 219 (2017) 126-131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for hamiltonicity of 2-connected graphs.  ...  If G is {P 7 , D}-free or {P 7 , H}-free, then G is hamiltonian. Corollary 8 (Ning [29] ). Let G be a 2-connected, claw-f-heavy graph.  ... 
doi:10.7151/dmgt.2170 fatcat:pcpeongzezc7lg37tyazctgdam

Some problems related to hamiltonian line graphs [chapter]

2007 Proceedings of the International Conference on Complex Geometry and Related Fields  
Part of this paper summarizes some of the recent developments in the study of hamiltonian line graphs and the related hamiltonian claw-free graphs.  ...  Definitions and Terminology Graphs considered here are finite and loopless. Unless otherwise noted, we follow [2] for notations and terms.  ...  On the other hand, we shall check that each G(k) is claw-free 3-connected (hence 3-edge-connected) and N 2 -locally connected. Since line graphs are claw-free, G(k) must also be claw-free.  ... 
doi:10.1090/amsip/039/09 fatcat:pxde4ptk7jfptarou6gs2f5iqi

Hamilton Circuits and Essential Girth of Claw Free Graphs

Zhengke Miao, Xiaofeng Wang, Cun-Quan Zhang
2015 Graphs and Combinatorics  
In this paper, we prove that every 2-connected {K 1,3 , N 1,1,g e (G)−4 }-free (and {K 1,3 , N 1,0,g e (G)−3 }-free) graph G contains a Hamilton circuit.  ...  Abstract Let G be a K 1,3 -free graph. A circuit of G is essential if it contains a non-locally connected vertex v and passes through both components of N (v).  ...  Here is the main theorem of this paper. (2) If a 2-connected graph G is claw-free and N 1,0,g e (G)−3 -free, then G contains a Hamilton circuit (see Fig. 2 ).  ... 
doi:10.1007/s00373-015-1559-9 fatcat:ariofyhwzve3jpvg6pkmuligxu

Hamiltonicity of 3-connected quasi-claw-free graphs

Rao Li
2003 Discrete Mathematics  
A graph G is called quasi-claw-free if it satisÿes the property: . Let G be a 3-connected quasi-claw-free graph of order n. If (G) ¿ (n + 5)=5, then G is hamiltonian.  ...  If H is not hamilton-connected, then |V (C)| ¿ 4 (G) − 5. Proof of Theorem 2 Proof of Theorem 2. Let G be a 3-connected quasi-claw-free nonhamiltonian graph satisfying the conditions in Theorem 2.  ...  Ainouche [1] extended a variety of results, in particular, hamiltonian results on claw-free graphs to quasi-claw-free graphs.  ... 
doi:10.1016/s0012-365x(02)00882-8 fatcat:kkleoznz5vgzze7fyqcrmp5kr4
« Previous Showing results 1 — 15 out of 715 results