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Connected Vertex Cover on AT-Free Graphs

Authors Joydeep Mukherjee, Tamojit Saha

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Joydeep Mukherjee
  • Ramakrishna Mission Vivekananda Educational and Research Institute, Belur, India
Tamojit Saha
  • Ramakrishna Mission Vivekananda Educational and Research Institute, Belur, India
  • Institute of Advancing Intelligence, TCG CREST, Kolkata, India

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Joydeep Mukherjee and Tamojit Saha. Connected Vertex Cover on AT-Free Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 54:1-54:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.54

Abstract

Asteroidal Triple (AT) in a graph is an independent set of three vertices such that every pair of them has a path between them avoiding the neighbourhood of the third. A graph is called AT-free if it does not contain any asteroidal triple. A connected vertex cover of a graph is a subset of its vertices which contains at least one endpoint of each edge and induces a connected subgraph. Settling the complexity of computing a minimum connected vertex cover in an AT-free graph was mentioned as an open problem in Escoffier et al. [Escoffier et al., 2010]. In this paper we answer the question by presenting an exact polynomial time algorithm for computing a minimum connected vertex cover problem on AT-free graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Graph Algorithm
  • AT-free graphs
  • Connected Vertex Cover
  • Optimization

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