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RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.59
On the Power of Choice for k-Colorability of Random Graphs

Authors: Varsha Dani, Diksha Gupta, and Thomas P. Hayes

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

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.
Cite as

Varsha Dani, Diksha Gupta, and Thomas P. Hayes. On the Power of Choice for k-Colorability of Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.59},
  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}
}
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