TY - GEN

T1 - Vertex Deletion on Split Graphs

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

AU - Choudhary, Pratibha

AU - Jain, Pallavi

AU - Krithika, R.

AU - Sahlot, Vibha

N1 - Funding Information:
We thank Saket Saurabh for his invaluable advice and several helpful suggestions. P. Jain— Supported by SERB-NPDF fellowship (PDF/2016/003508) of DST, India.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In vertex deletion problems on graphs, the task is to find a set of minimum number of vertices whose deletion results in a graph with some specific property. The class of vertex deletion problems contains several classical optimization problems, and has been studied extensively in algorithm design. Recently, there was a study on vertex deletion problems on split graphs. One of the results shown was that transforming a split graph into a block graph and a threshold graph using minimum number of vertex deletions is NP-hard. We call the decision version of these problems as Split to Block Vertex Deletion (SBVD) and Split to Threshold Vertex Deletion (STVD), respectively. In this paper, we study these problems in the realm of parameterized complexity with respect to the number of vertex deletions k as parameter. These problems are “implicit” 4-Hitting Set, and thus admit an algorithm with running time, a kernel with vertices, and a 4-approximation algorithm. In this paper, we exploit the structure of the input graph to obtain a kernel for SBVD with vertices and FPT algorithms for SBVD and STVD with running times and.

AB - In vertex deletion problems on graphs, the task is to find a set of minimum number of vertices whose deletion results in a graph with some specific property. The class of vertex deletion problems contains several classical optimization problems, and has been studied extensively in algorithm design. Recently, there was a study on vertex deletion problems on split graphs. One of the results shown was that transforming a split graph into a block graph and a threshold graph using minimum number of vertex deletions is NP-hard. We call the decision version of these problems as Split to Block Vertex Deletion (SBVD) and Split to Threshold Vertex Deletion (STVD), respectively. In this paper, we study these problems in the realm of parameterized complexity with respect to the number of vertex deletions k as parameter. These problems are “implicit” 4-Hitting Set, and thus admit an algorithm with running time, a kernel with vertices, and a 4-approximation algorithm. In this paper, we exploit the structure of the input graph to obtain a kernel for SBVD with vertices and FPT algorithms for SBVD and STVD with running times and.

KW - Approximation algorithms

KW - Kernelization

KW - Parameterized algorithms

KW - Split graphs

KW - Vertex deletion problems

UR - http://www.scopus.com/inward/record.url?scp=85066906937&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17402-6_14

DO - 10.1007/978-3-030-17402-6_14

M3 - Conference contribution

AN - SCOPUS:85066906937

SN - 9783030174019

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

SP - 161

EP - 173

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

A2 - Heggernes, Pinar

PB - Springer Verlag

Y2 - 27 May 2019 through 29 May 2019

ER -