Degree-constrained decompositions of graphs: Bounded treewidth and planarity

Cristina Bazgan, Z. Tuza, Daniel Vanderpooten

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)389-395
Number of pages7
JournalTheoretical Computer Science
Volume355
Issue number3
DOIs
Publication statusPublished - Apr 14 2006

Fingerprint

Planarity
Bounded Treewidth
Decomposition
Decompose
Graph in graph theory
Polynomials
Degree Condition
Polynomial Time Approximation Scheme
Vertex of a graph
Planar graph
Polynomial-time Algorithm
Subgraph

Keywords

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

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

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

In: Theoretical Computer Science, Vol. 355, No. 3, 14.04.2006, p. 389-395.

Research output: Contribution to journalArticle

Bazgan, Cristina ; Tuza, Z. ; Vanderpooten, Daniel. / Degree-constrained decompositions of graphs : Bounded treewidth and planarity. In: Theoretical Computer Science. 2006 ; Vol. 355, No. 3. pp. 389-395.
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