Quadratic Vertex Kernel for Split Vertex Deletion

Akanksha Agrawal, Sushmita Gupta, Pallavi Jain, R. Krithika

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


A graph is called a split graph if its vertex set can be partitioned into a clique and an independent set. Split graphs have rich mathematical structure and interesting algorithmic properties making it one of the most well-studied special graph classes. In the Split Vertex Deletion(SVD) problem, given a graph and a positive integer k, the objective is to test whether there exists a subset of at most k vertices whose deletion results in a split graph. In this paper, we design a kernel for this problem with vertices, improving upon the previous cubic bound known. Also, by giving a simple reduction from the Vertex Cover problem, we establish that SVD does not admit a kernel with edges, for any, unless.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings
EditorsPinar Heggernes
PublisherSpringer Verlag
Number of pages12
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


  • Kernel lower bound
  • Kernelization
  • Parameterized Complexity
  • Split Vertex Deletion

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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