Graph factors and factorization: 1985–2003: A survey

Plummer, Michael D.

doi:10.1016/j.disc.2005.11.059

Cited by 113 publications

(65 citation statements)

References 255 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If a graph G is claw-free, 3-connected and has δ ≥ 4, then G has a 2-factor with at most 2n/15 components [10]. For more on graph factors we refer the reader to the survey [16].…”

Section: Theorem 1 ([2 4])mentioning

confidence: 99%

See 1 more Smart Citation

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

Broersma

Paulusma

Yoshimoto

2009

Graphs and Combinatorics

View full text Add to dashboard Cite

(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.

show abstract

“…If a graph G is claw-free, 3-connected and has δ ≥ 4, then G has a 2-factor with at most 2n/15 components [10]. For more on graph factors we refer the reader to the survey [16].…”

Section: Theorem 1 ([2 4])mentioning

confidence: 99%

“…Finally, claw-free graphs form a rich class containing all line graphs and the class of complements of triangle-free graphs. Research on claw-free graphs and graph factors are both considerably popular areas within graph theory, as witnessed by the survey papers [7] and [16], respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Broersma

Paulusma

Yoshimoto

2009

Graphs and Combinatorics

View full text Add to dashboard Cite

show abstract

“…In their surveys, Akiyama and Kano [1], and more recently, Plummer [12], include multiple results describing classes of graphs for which k-factors exist. In some cases an algorithm that computes such a k-factor is also given.…”

Section: Previous Workmentioning

confidence: 99%

An algorithm for computing simple k-factors

Meijer

Núòez-Rodríguez

Rappaport

2009

Information Processing Letters

View full text Add to dashboard Cite

A k-factor of graph G is defined as a k-regular spanning subgraph of G. For instance, a 2-factor of G is a set of cycles that span G. 2-factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5,4,6,14]. We define a simple 2-factor as a 2-factor without degenerate cycles. In general, simple k-factors are defined as k-regular spanning subgraphs where no edge is used more than once. We propose a new algorithm for computing simple k-factors for all values of k ≥ 2.

show abstract

“…Note as well that if G has a 2-factor F, then G has a 2-proper partition, as each component of F induces a hamiltonian, and therefore 2-connected, graph. Consequently, the problem of determining if G has a 2-proper partition can also be viewed as an extension of the 2-factor problem [1,15], which is itself one of the most natural generalizations of the hamiltonian problem [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Partitioning a Graph into Highly Connected Subgraphs

Borozan

Ferrara

Fujita

et al. 2015

Journal of Graph Theory

View full text Add to dashboard Cite

Given k ≥ 1, a k-proper partition of a graph G is a partition P of V (G) such that each part P of P induces a k-connected subgraph of G. We prove that if G is a graph of order n such that δ(G) ≥ √ n, then G has a 2-proper partition with at most n/δ(G) parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that if G is a graph of order n with minimum degree

show abstract

Graph factors and factorization: 1985–2003: A survey

Cited by 113 publications

References 255 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

An algorithm for computing simple k-factors

Partitioning a Graph into Highly Connected Subgraphs

Contact Info

Product

Resources

About