Packing tree degree sequences

Kristóf Bérczi, Zoltán Király, Changshuo Liu, I. Miklós

Research output: Contribution to journalArticle

Abstract

Special cases of the edge disjoint realizations of two tree degree sequences are considered in this paper. We show that if there is no node which have degree one in both degree sequences, then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove that two tree degree sequences always have edge-disjoint realizations if each vertex is a leaf in at least one of the trees. We also show that the edge-disjoint realization problem is in P for an arbitrary number of tree sequences with the property that each vertex is a non-leaf in at most one of the trees. On the other hand, we show that the following problem is already NP-complete: given two graphical degree sequences D1 and D2 such that D2 is a tree degree sequence, decide if there exist edge-disjoint realizations of D1 and D2 where the realization of D2 does not need to be a tree. Finally, we show that efficient approximations for the number of solutions as well as an almost uniform sampler exist for two tree degree sequences if each vertex is a leaf in at least one of the trees.

Original languageEnglish
Pages (from-to)11-18
Number of pages8
JournalInformatica (Slovenia)
Volume43
Issue number1
DOIs
Publication statusPublished - Jan 1 2019

Fingerprint

Degree Sequence
Packing
Disjoint
Vertex of a graph
Leaves
Caterpillar
Probabilistic Methods
Number of Solutions
NP-complete problem
Arbitrary

Keywords

  • Degree sequences
  • Edge-disjoint realizations
  • Packing spanning trees
  • Uniform sampling

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computer Science Applications
  • Artificial Intelligence

Cite this

Packing tree degree sequences. / Bérczi, Kristóf; Király, Zoltán; Liu, Changshuo; Miklós, I.

In: Informatica (Slovenia), Vol. 43, No. 1, 01.01.2019, p. 11-18.

Research output: Contribution to journalArticle

Bérczi, K, Király, Z, Liu, C & Miklós, I 2019, 'Packing tree degree sequences', Informatica (Slovenia), vol. 43, no. 1, pp. 11-18. https://doi.org/10.31449/inf.v43i1.2675
Bérczi, Kristóf ; Király, Zoltán ; Liu, Changshuo ; Miklós, I. / Packing tree degree sequences. In: Informatica (Slovenia). 2019 ; Vol. 43, No. 1. pp. 11-18.
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