Quadratic vertex kernel for split vertex deletion

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 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 O(k2) vertices, improving upon the previous cubic bound known. Also, by giving a simple reduction from the VERTEX COVER problem, we establish that SPLIT VERTEX DELETION does not admit a kernel with O(k2−ϵ) edges, for any ϵ>0, unless NP⊆coNP/poly.

Original languageEnglish
Pages (from-to)164-172
Number of pages9
JournalTheoretical Computer Science
StatePublished - 12 Sep 2020
Externally publishedYes


  • Kernelization
  • Split graph
  • Vertex deletion

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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