Regular factors in <i>K</i><sub>1,3</sub>‐free graphs

Choudum, S. A.; Paulraj, M. S.

doi:10.1002/jgt.3190150304

Cited by 27 publications

(16 citation statements)

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“…Results of both Choudum & Paulraj [2] and Egawa & Ota [4] imply that a moderate minimum degree condition already guarantees that a claw-free graph contains a 2-factor.…”

Section: Known Resultsmentioning

confidence: 95%

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Broersma

Paulusma

Yoshimoto

2009

Graphs and Combinatorics

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(2009) 'Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs. ', Graphs and combinatorics., 25 (4). pp. 427-460. Further information on publisher's website:http://dx.doi.org/10.1007/s00373-009-0855-7Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00373-009-0855-7Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. Let G be a claw-free graph with order n and minimum degree δ. We improve results of Faudree et al. and Gould & Jacobson, and solve two open problems by proving the following two results. If δ = 4, then G has a 2-factor with at most (5n − 14)/18 components, unless G belongs to a finite class of exceptional graphs. If δ ≥ 5, then G has a 2-factor with at most (n − 3)/(δ − 1) components, unless G is a complete graph. These bounds are best possible in the sense that we cannot replace 5/18 by a smaller quotient and we cannot replace δ − 1 by δ, respectively.

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“…Results of both Choudum & Paulraj [2] and Egawa & Ota [4] imply that a moderate minimum degree condition already guarantees that a claw-free graph contains a 2-factor.…”

Section: Known Resultsmentioning

confidence: 95%

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Broersma

Paulusma

Yoshimoto

2009

Graphs and Combinatorics

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“…It follows from either [2] or [3] that every claw-free graph G with δ(G) 4 has a 2-factor. Yoshimoto [9] showed that a claw-free graph G with δ(G) 3 has also a 2-factor if, additionally, G is 2-connected.…”

Section: Gould and Hynds Inmentioning

confidence: 99%

Two operations on a graph preserving the (non)existence of 2-factors in its line graph

Lai

et al. 2014

Czech Math J

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Abstract. Let G = (V (G), E(G)) be a graph. Gould and Hynds (1999) showed a wellknown characterization of G by its line graph L(G) that has a 2-factor. In this paper, by defining two operations, we present a characterization for a graph G to have a 2-factor in its line graph2}] is connected. By applying the new characterization, we prove that every claw-free graph in which every edge lies on a cycle of length at most five and in which every vertex of degree two that lies on a triangle has two N 2 -locally connected adjacent neighbors, has a 2-factor. This result generalizes the previous results in papers : Li, Liu (1995) and Tian, Xiong, Niu (2012), and is the best possible.

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“…[8], Lai, Li, Shao and Xiong [7]) Let G be a clawfree graph. If G has a connected even factor H, then G has a connected even [2,4]…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…From the results of Choudum and Paulraj [2], and Egawa and Ota [3], one can deduce that every claw-free graph with minimum degree at least 4 has a 2-factor. Very recently, Yoshimoto show that the minimum degree can be reduced if we increase its connectivity.…”

Section: Introductionmentioning

confidence: 99%

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Even Factors with Degree at Most Four in Claw-Free Graphs

Xiong

2007

Computational Science – ICCS 2007

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Regular factors in K_1,3‐free graphs

Abstract: We show that every connected Kl,sfree graph with minimum degree at least 2k contains a k-factor and construct connected K1,3-free graphs with minimum degree k + O(dk) that have no k-factor.

Cited by 27 publications

References 10 publications

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Two operations on a graph preserving the (non)existence of 2-factors in its line graph

Even Factors with Degree at Most Four in Claw-Free Graphs

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Regular factors in K1,3‐free graphs

Abstract: We show that every connected Kl,sfree graph with minimum degree at least 2k contains a k-factor and construct connected K1,3-free graphs with minimum degree k + O(dk) that have no k-factor.

Cited by 27 publications

References 10 publications

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Sharp Upper Bounds on the Minimum Number of Components of 2-factors in Claw-free Graphs

Two operations on a graph preserving the (non)existence of 2-factors in its line graph

Even Factors with Degree at Most Four in Claw-Free Graphs

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Product

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Regular factors in K_1,3‐free graphs