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 -