TY - JOUR
T1 - Quadratic vertex kernel for split vertex deletion
AU - Agrawal, Akanksha
AU - Gupta, Sushmita
AU - Jain, Pallavi
AU - Krithika, R.
N1 - Funding Information:
We are thankful to the reading course headed by Saket Saurabh, held at Institute of Mathematical Sciences, during which the problem was suggested for research. The first three authors during the work were supported by the ERC Consolidator Grant SYSTEMATIC-GRAPH (No. 725978 ) of the European Research Council ; Research Council of Norway , Toppforsk project (No. 274526 ); and SERB-NPDF fellowship ( PDF/2016/003508 ) of Department of Science and Technology , India, respectively.
Funding Information:
We are thankful to the reading course headed by Saket Saurabh, held at Institute of Mathematical Sciences, during which the problem was suggested for research. The first three authors during the work were supported by the ERC Consolidator Grant SYSTEMATIC-GRAPH (No. 725978) of the European Research Council; Research Council of Norway, Toppforsk project (No. 274526); and SERB-NPDF fellowship (PDF/2016/003508) of Department of Science and Technology, India, respectively.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/9/12
Y1 - 2020/9/12
N2 - 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.
AB - 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.
KW - Kernelization
KW - Split graph
KW - Vertex deletion
UR - http://www.scopus.com/inward/record.url?scp=85085938914&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2020.06.001
DO - 10.1016/j.tcs.2020.06.001
M3 - Article
AN - SCOPUS:85085938914
SN - 0304-3975
VL - 833
SP - 164
EP - 172
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -