License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.27
URN: urn:nbn:de:0030-drops-154609
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Bar-Noy, Amotz ; Peleg, David ; Rawitz, Dror ; Yehezkel, Elad

Selected Neighbor Degree Forest Realization

LIPIcs-ISAAC-2021-27.pdf (0.8 MB)


The classical degree realization problem is defined as follows: Given a sequence d̄ = (d_1,…,d_n) of positive integers, construct an n-vertex graph in which each vertex u_i has degree d_i (or decide that no such graph exists). In this article, we present and study the related selected neighbor degree realization problem, which requires that each vertex u_i of G has a neighbor of degree d_i. We solve the problem when G is required to be acyclic (i.e., a forest), and present a sufficient and necessary condition for a given sequence to be realizable.

BibTeX - Entry

  author =	{Bar-Noy, Amotz and Peleg, David and Rawitz, Dror and Yehezkel, Elad},
  title =	{{Selected Neighbor Degree Forest Realization}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-154609},
  doi =		{10.4230/LIPIcs.ISAAC.2021.27},
  annote =	{Keywords: network realization, graph algorithms, lower bound}

Keywords: network realization, graph algorithms, lower bound
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

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