TY - GEN

T1 - Quadratic Vertex Kernel for Split Vertex Deletion

AU - Agrawal, Akanksha

AU - Gupta, Sushmita

AU - Jain, Pallavi

AU - Krithika, R.

N1 - Funding Information:
The first three authors are 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 DST, India, respectively.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

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(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.

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(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.

KW - Kernel lower bound

KW - Kernelization

KW - Parameterized Complexity

KW - Split Vertex Deletion

UR - http://www.scopus.com/inward/record.url?scp=85066906601&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17402-6_1

DO - 10.1007/978-3-030-17402-6_1

M3 - Conference contribution

AN - SCOPUS:85066906601

SN - 9783030174019

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 12

BT - Algorithms and Complexity - 11th International Conference, CIAC 2019, Proceedings

A2 - Heggernes, Pinar

PB - Springer Verlag

T2 - 11th International Conference on Algorithms and Complexity, CIAC 2019

Y2 - 27 May 2019 through 29 May 2019

ER -