Abstract
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(8 knO ( 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).
Original language | English |
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Pages (from-to) | 62-100 |
Number of pages | 39 |
Journal | Theory of Computing Systems |
Volume | 64 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2020 |
Keywords
- Above guarantee parameterization
- Fixed-parameter tractable algorithm
- Max-Cut
- Polynomial kernel
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics