Well quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications

Michael R. Fellows; Danny Hermelin; Frances A. Rosamond

doi:https://doi.org/10.1007/s00453-011-9545-y

Well quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications

Michael R. Fellows, Danny Hermelin, Frances A. Rosamond

Research output: Contribution to journal › Article › peer-review

Abstract

We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.

Original language	American English
Pages (from-to)	3-18
Number of pages	16
Journal	Algorithmica
Volume	64
Issue number	1
DOIs	https://doi.org/10.1007/s00453-011-9545-y
State	Published - 1 Sep 2012
Externally published	Yes

Keywords

Bounded circumference graphs
Bounded feedback vertex set graphs
Bounded vertex cover graphs
Exact algorithms
Geometric graph recognition
Meta-algorithms
Parameterized complexity
String graphs
Tree decomposition
Treewidth
Well quasi order

All Science Journal Classification (ASJC) codes

General Computer Science
Applied Mathematics
Computer Science Applications

Access to Document

https://doi.org/10.1007/s00453-011-9545-y

Cite this

@article{5c5548eaa5304dee9c51c182f147f7e2,

title = "Well quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications",

abstract = "We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.",

keywords = "Bounded circumference graphs, Bounded feedback vertex set graphs, Bounded vertex cover graphs, Exact algorithms, Geometric graph recognition, Meta-algorithms, Parameterized complexity, String graphs, Tree decomposition, Treewidth, Well quasi order",

author = "Fellows, {Michael R.} and Danny Hermelin and Rosamond, {Frances A.}",

note = "Funding Information: Research supported by the Australian Research Council.",

year = "2012",

month = sep,

day = "1",

doi = "https://doi.org/10.1007/s00453-011-9545-y",

language = "American English",

volume = "64",

pages = "3--18",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Well quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications

AU - Fellows, Michael R.

AU - Hermelin, Danny

AU - Rosamond, Frances A.

N1 - Funding Information: Research supported by the Australian Research Council.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.

AB - We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.

KW - Bounded circumference graphs

KW - Bounded feedback vertex set graphs

KW - Bounded vertex cover graphs

KW - Exact algorithms

KW - Geometric graph recognition

KW - Meta-algorithms

KW - Parameterized complexity

KW - String graphs

KW - Tree decomposition

KW - Treewidth

KW - Well quasi order

UR - http://www.scopus.com/inward/record.url?scp=84861455469&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s00453-011-9545-y

DO - https://doi.org/10.1007/s00453-011-9545-y

M3 - Article

SN - 0178-4617

VL - 64

SP - 3

EP - 18

JO - Algorithmica

JF - Algorithmica

IS - 1

ER -

Well quasi orders in subclasses of bounded treewidth graphs and their algorithmic applications

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this