Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Fomin, Fedor V.; Golovach, Petr A.; Sagunov, Danil; Simonov, Kirill https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-169935
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Longest Cycle Above Erdős-Gallai Bound

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Abstract

In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a cycle of length at least ad(G). We provide an algorithm that for k ≥ 0 in time 2^𝒪(k)⋅n^𝒪(1) decides whether a 2-connected n-vertex graph G contains a cycle of length at least ad(G)+k. This resolves an open problem explicitly mentioned in several papers. The main ingredients of our algorithm are new graph-theoretical results interesting on their own.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs.ESA.2022.55,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Longest Cycle Above Erd\H{o}s-Gallai Bound}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16993},
  URN =		{urn:nbn:de:0030-drops-169935},
  doi =		{10.4230/LIPIcs.ESA.2022.55},
  annote =	{Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, Erd\H{o}s and Gallai theorem}
}

Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, Erdős and Gallai theorem
Seminar: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue date: 2022
Date of publication: 01.09.2022


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