English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The $k$-cut problem asks, given a connected graph $G$ and a positive integer$k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$connected components. We give the first polynomial-time algorithm withapproximation factor $2-\epsilon$ (with constant $\epsilon > 0$) for the$k$-cut problem in planar and minor-free graphs. Applying more complextechniques, we further improve our method and give a polynomial-timeapproximation scheme for the $k$-cut problem in both planar and minor-freegraphs. Despite persistent effort, to the best of our knowledge, this is thefirst improvement for the $k$-cut problem over standard approximation factor of$2$ in any major class of graphs.

Polynomial-time Approximation Scheme for Minimum k-cut in Planar and Minor-free Graphs