## Abstract

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(k^{2}) 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(k^{2−ϵ}) edges, for any ϵ>0, unless NP⊆coNP/poly.

Original language | English |
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Pages (from-to) | 164-172 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 833 |

DOIs | |

State | Published - 12 Sep 2020 |

Externally published | Yes |

## Keywords

- Kernelization
- Split graph
- Vertex deletion

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science