### Abstract

We study the problem of decomposing the vertex set V of a graph into two nonempty parts V1,V2 which induce subgraphs where each vertex v∈V1 has degree at least a(v) inside V1 and each v∈V2 has degree at least b(v) inside V2. We give a polynomial-time algorithm for graphs with bounded treewidth which decides if a graph admits a decomposition, and gives such a decomposition if it exists. This result and its variants are then applied to designing polynomial-time approximation schemes for planar graphs where a decomposition does not necessarily exist but the local degree conditions should be met for as many vertices as possible.

Original language | English |
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Pages (from-to) | 389-395 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 355 |

Issue number | 3 |

DOIs | |

Publication status | Published - Apr 14 2006 |

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### Keywords

- Graph decomposition
- Planar graph
- Polynomial algorithm
- PTAS
- Treewidth

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*355*(3), 389-395. https://doi.org/10.1016/j.tcs.2006.01.024

**Degree-constrained decompositions of graphs : Bounded treewidth and planarity.** / Bazgan, Cristina; Tuza, Z.; Vanderpooten, Daniel.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 355, no. 3, pp. 389-395. https://doi.org/10.1016/j.tcs.2006.01.024

}

TY - JOUR

T1 - Degree-constrained decompositions of graphs

T2 - Bounded treewidth and planarity

AU - Bazgan, Cristina

AU - Tuza, Z.

AU - Vanderpooten, Daniel

PY - 2006/4/14

Y1 - 2006/4/14

N2 - We study the problem of decomposing the vertex set V of a graph into two nonempty parts V1,V2 which induce subgraphs where each vertex v∈V1 has degree at least a(v) inside V1 and each v∈V2 has degree at least b(v) inside V2. We give a polynomial-time algorithm for graphs with bounded treewidth which decides if a graph admits a decomposition, and gives such a decomposition if it exists. This result and its variants are then applied to designing polynomial-time approximation schemes for planar graphs where a decomposition does not necessarily exist but the local degree conditions should be met for as many vertices as possible.

AB - We study the problem of decomposing the vertex set V of a graph into two nonempty parts V1,V2 which induce subgraphs where each vertex v∈V1 has degree at least a(v) inside V1 and each v∈V2 has degree at least b(v) inside V2. We give a polynomial-time algorithm for graphs with bounded treewidth which decides if a graph admits a decomposition, and gives such a decomposition if it exists. This result and its variants are then applied to designing polynomial-time approximation schemes for planar graphs where a decomposition does not necessarily exist but the local degree conditions should be met for as many vertices as possible.

KW - Graph decomposition

KW - Planar graph

KW - Polynomial algorithm

KW - PTAS

KW - Treewidth

UR - http://www.scopus.com/inward/record.url?scp=33644918357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644918357&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2006.01.024

DO - 10.1016/j.tcs.2006.01.024

M3 - Article

AN - SCOPUS:33644918357

VL - 355

SP - 389

EP - 395

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 3

ER -