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.ICALP.2021.105
URN: urn:nbn:de:0030-drops-141746
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14174/
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Pettie, Seth ; Yin, Longhui

The Structure of Minimum Vertex Cuts

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LIPIcs-ICALP-2021-105.pdf (1 MB)


Abstract

In this paper we continue a long line of work on representing the cut structure of graphs. We classify the types of minimum vertex cuts, and the possible relationships between multiple minimum vertex cuts.
As a consequence of these investigations, we exhibit a simple O(κ n)-space data structure that can quickly answer pairwise (κ+1)-connectivity queries in a κ-connected graph. We also show how to compute the "closest" κ-cut to every vertex in near linear Õ(m+poly(κ)n) time.

BibTeX - Entry

@InProceedings{pettie_et_al:LIPIcs.ICALP.2021.105,
  author =	{Pettie, Seth and Yin, Longhui},
  title =	{{The Structure of Minimum Vertex Cuts}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{105:1--105:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14174},
  URN =		{urn:nbn:de:0030-drops-141746},
  doi =		{10.4230/LIPIcs.ICALP.2021.105},
  annote =	{Keywords: Graph theory, vertex connectivity, data structures}
}

Keywords: Graph theory, vertex connectivity, data structures
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021


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