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.APPROX/RANDOM.2021.59
URN: urn:nbn:de:0030-drops-147527
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14752/
Go to the corresponding LIPIcs Volume Portal

Dani, Varsha ; Gupta, Diksha ; Hayes, Thomas P.

On the Power of Choice for k-Colorability of Random Graphs

pdf-format:
LIPIcs-APPROX59.pdf (0.7 MB)

Abstract

In an r-choice Achlioptas process, random edges are generated r at a time, and an online strategy is used to select one of them for inclusion in a graph. We investigate the problem of whether such a selection strategy can shift the k-colorability transition; that is, the number of edges at which the graph goes from being k-colorable to non-k-colorable.
We show that, for k ≥ 9, two choices suffice to delay the k-colorability threshold, and that for every k ≥ 2, six choices suffice.

BibTeX - Entry

@InProceedings{dani_et_al:LIPIcs.APPROX/RANDOM.2021.59,
  author =	{Dani, Varsha and Gupta, Diksha and Hayes, Thomas P.},
  title =	{{On the Power of Choice for k-Colorability of Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{59:1--59:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14752},
  URN =		{urn:nbn:de:0030-drops-147527},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.59},
  annote =	{Keywords: Random graphs, Achlioptas Processes, Phase Transition, Graph Colorability}
}

Keywords: Random graphs, Achlioptas Processes, Phase Transition, Graph Colorability
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Issue Date: 2021
Date of publication: 15.09.2021

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI