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Quadratic vertex kernel for split vertex deletion
A. Agrawal, S. Gupta, , R. Krithika
Published in Elsevier B.V.
Volume: 833
Pages: 164 - 172
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. © 2020 Elsevier B.V.
About the journal
JournalData powered by TypesetTheoretical Computer Science
PublisherData powered by TypesetElsevier B.V.