TY - GEN

T1 - Faster parameterized algorithms for deletion to split graphs

AU - Ghosh, Esha

AU - Kolay, Sudeshna

AU - Kumar, Mrinal

AU - Misra, Pranabendu

AU - Panolan, Fahad

AU - Rai, Ashutosh

AU - Ramanujan, M. S.

PY - 2012/7/4

Y1 - 2012/7/4

N2 - An undirected graph is said to be split if its vertex set can be partitioned into two sets such that the subgraph induced on one of them is a complete graph and the subgraph induced on the other is an independent set. We study the problem of deleting the minimum number of vertices or edges from a given input graph so that the resulting graph is split.We initiate a systematic study and give efficient fixed-parameter algorithms and polynomial sized kernels for the problem. More precisely, 1 for Split Vertex Deletion, the problem of determining whether there are k vertices whose deletion results in a split graph, we give an algorithm improving on the previous best bound of . We also give an -sized kernel for the problem. 2 For Split Edge Deletion, the problem of determining whether there are k edges whose deletion results in a split graph, we give an algorithm. We also prove the existence of an kernel. In addition, we note that our algorithm for Split Edge Deletion adds to the small number of subexponential parameterized algorithms not obtained through bidimensionality, and on general graphs.

AB - An undirected graph is said to be split if its vertex set can be partitioned into two sets such that the subgraph induced on one of them is a complete graph and the subgraph induced on the other is an independent set. We study the problem of deleting the minimum number of vertices or edges from a given input graph so that the resulting graph is split.We initiate a systematic study and give efficient fixed-parameter algorithms and polynomial sized kernels for the problem. More precisely, 1 for Split Vertex Deletion, the problem of determining whether there are k vertices whose deletion results in a split graph, we give an algorithm improving on the previous best bound of . We also give an -sized kernel for the problem. 2 For Split Edge Deletion, the problem of determining whether there are k edges whose deletion results in a split graph, we give an algorithm. We also prove the existence of an kernel. In addition, we note that our algorithm for Split Edge Deletion adds to the small number of subexponential parameterized algorithms not obtained through bidimensionality, and on general graphs.

UR - http://www.scopus.com/inward/record.url?scp=84863098119&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31155-0_10

DO - 10.1007/978-3-642-31155-0_10

M3 - Conference contribution

AN - SCOPUS:84863098119

SN - 9783642311543

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

SP - 107

EP - 118

BT - Algorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings

T2 - 13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012

Y2 - 4 July 2012 through 6 July 2012

ER -