Max-Cut Parameterized above the Edwards-Erdős Bound

Robert Crowston, Mark Jones, Matthias Mnich

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We study the boundary of tractability for the max-cut problem in graphs. Our main result shows that max-cut above the edwards-erdos bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size \frac{m}{2} + \frac{n-1}{4} + k \frac{m}{2} + \frac{n-1}{4} + k in time 2 o(k)·n 4, or decides that no such cut exists.this answers a long-standing open question from parameterized complexity that has been posed a number of times over the past 15 years.our algorithm is asymptotically optimal, under the exponential time hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.
Original languageEnglish
Title of host publicationAutomata, Languages and Programming
Subtitle of host publication39th International Colloquium, ICALP 2012, Warwick, UK, July 2012, Proceedings, Part I
EditorsArtur Czumaj, Kurt Mehlhorn, Andrew Pitts, Roger Wattenhofer
ISBN (Electronic)978-3-642-31594-7
ISBN (Print)978-3-642-31593-0
Publication statusPublished - 2012
Externally publishedYes

Publication series

SeriesLecture Notes in Computer Science

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