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On some combinatorial problems in cographs

  • Harshita KonaEmail author
  • N. Sadagopan
Article
  • 27 Downloads

Abstract

The family of graphs that can be constructed from isolated vertices by disjoint union and graph join operations are called cographs. These graphs can be represented in a tree-like representation termed parse tree or cotree. In this paper, we study some popular combinatorial problems restricted to cographs. We first present a structural characterization of minimal vertex separators in cographs. Further, we show that listing all minimal vertex separators and finding some constrained vertex separators are linear-time solvable in cographs. We propose polynomial-time algorithms for some connectivity augmentation problems and its variants in cographs, preserving the cograph property. Finally, using the dynamic programming paradigm, we present a generic framework to solve classical optimization problems such as the longest path, the Steiner path and the minimum leaf spanning tree problems restricted to cographs and our framework yields polynomial-time algorithms for the three problems.

Keywords

Cographs Augmentation problems Vertex separators Hamiltonian path Longest path Steiner path Minimum leaf spanning tree 

Notes

Funding

This work is partially supported by DST-ECRA project - ECR/2017/001442.

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Copyright information

© Indian Institute of Technology Madras 2019

Authors and Affiliations

  1. 1.Indian Institute of Information Technology Design and Manufacturing, KancheepuramChennaiIndia

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