TY - GEN

T1 - Max-cut above spanning tree is fixed-parameter tractable

AU - Madathil, Jayakrishnan

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Every connected graph on n vertices has a cut of size at least n − 1. We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least n − 1 + k. We show that Max-Cut-AST admits an algorithm that runs in time O(8knO(1), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size O(k5).

AB - Every connected graph on n vertices has a cut of size at least n − 1. We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least n − 1 + k. We show that Max-Cut-AST admits an algorithm that runs in time O(8knO(1), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size O(k5).

UR - http://www.scopus.com/inward/record.url?scp=85048048614&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-90530-3_21

DO - 10.1007/978-3-319-90530-3_21

M3 - Conference contribution

AN - SCOPUS:85048048614

SN - 9783319905297

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

SP - 244

EP - 256

BT - Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings

A2 - Podolskii, Vladimir V.

A2 - Fomin, Fedor V.

PB - Springer Verlag

T2 - 13th International Computer Science Symposium in Russia, CSR 2018

Y2 - 6 June 2018 through 10 June 2018

ER -