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The Structure of Minimum Vertex Cuts

Authors Seth Pettie, Longhui Yin

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Author Details

Seth Pettie
  • University of Michigan, Ann Arbor, MI, USA
Longhui Yin
  • Tsinghua University, Beijing, China

Funding

  • Pettie, Seth: This work was supported by NSF grants CCF-1637546 and CCF-1815316.
  • Yin, Longhui: Supported by a grant from Tsinghua University.

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Seth Pettie and Longhui Yin. The Structure of Minimum Vertex Cuts. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 105:1-105:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.105

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Theory of computation → Data structures design and analysis
Keywords
  • Graph theory
  • vertex connectivity
  • data structures

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