Efficient algorithms for decomposing graphs under degree constraints

Cristina Bazgan, Z. Tuza, Daniel Vanderpooten

Research output: Article

16 Citations (Scopus)

Abstract

Stiebitz [Decomposing graphs under degree constraints, J. Graph Theory 23 (1996) 321-324] proved that if every vertex v in a graph G has degree d (v) ≥ a (v) + b (v) + 1 (where a and b are arbitrarily given nonnegative integer-valued functions) then G has a nontrivial vertex partition (A, B) such that dA (v) ≥ a (v) for every v ∈ A and dB (v) ≥ b (v) for every v ∈ B. Kaneko [On decomposition of triangle-free graphs under degree constraints, J. Graph Theory 27 (1998) 7-9] and Diwan [Decomposing graphs with girth at least five under degree constraints, J. Graph Theory 33 (2000) 237-239] strengthened this result, proving that it suffices to assume d (v) ≥ a + b (a, b ≥ 1) or just d (v) ≥ a + b - 1 (a, b ≥ 2) if G contains no cycles shorter than 4 or 5, respectively. The original proofs contain nonconstructive steps. In this paper we give polynomial-time algorithms that find such partitions. Constructive generalizations for k-partitions are also presented.

Original languageEnglish
Pages (from-to)979-988
Number of pages10
JournalDiscrete Applied Mathematics
Volume155
Issue number8
DOIs
Publication statusPublished - ápr. 15 2007

Fingerprint

Graph theory
Efficient Algorithms
Graph in graph theory
Partition
Vertex Partition
Triangle-free Graph
Girth
Polynomial-time Algorithm
Non-negative
Polynomials
Decomposition
Cycle
Decompose
Integer
Vertex of a graph

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Efficient algorithms for decomposing graphs under degree constraints. / Bazgan, Cristina; Tuza, Z.; Vanderpooten, Daniel.

In: Discrete Applied Mathematics, Vol. 155, No. 8, 15.04.2007, p. 979-988.

Research output: Article

Bazgan, Cristina ; Tuza, Z. ; Vanderpooten, Daniel. / Efficient algorithms for decomposing graphs under degree constraints. In: Discrete Applied Mathematics. 2007 ; Vol. 155, No. 8. pp. 979-988.
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