Vertex Deletion on Split Graphs: Beyond 4-Hitting Set

Pratibha Choudhary, Pallavi Jain, R. Krithika, Vibha Sahlot

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


In vertex deletion problems on graphs, the task is to find a set of minimum number of vertices whose deletion results in a graph with some specific property. The class of vertex deletion problems contains several classical optimization problems, and has been studied extensively in algorithm design. Recently, there was a study on vertex deletion problems on split graphs. One of the results shown was that transforming a split graph into a block graph and a threshold graph using minimum number of vertex deletions is NP-hard. We call the decision version of these problems as Split to Block Vertex Deletion (SBVD) and Split to Threshold Vertex Deletion (STVD), respectively. In this paper, we study these problems in the realm of parameterized complexity with respect to the number of vertex deletions k as parameter. These problems are “implicit” 4-Hitting Set, and thus admit an algorithm with running time, a kernel with vertices, and a 4-approximation algorithm. In this paper, we exploit the structure of the input graph to obtain a kernel for SBVD with vertices and FPT algorithms for SBVD and STVD with running times and.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings
EditorsPinar Heggernes
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783030174019
StatePublished - 1 Jan 2019
Externally publishedYes
Event11th International Conference on Algorithms and Complexity, CIAC 2019 - Rome, Italy
Duration: 27 May 201929 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11485 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th International Conference on Algorithms and Complexity, CIAC 2019


  • Approximation algorithms
  • Kernelization
  • Parameterized algorithms
  • Split graphs
  • Vertex deletion problems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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