Edge-Cuts and Rooted Spanning Trees

TL;DR

This paper presents a closed-form formula for determining the size of k-respecting cuts and shows that these can be computed solely from 2-respecting cuts, simplifying the analysis of graph cuts.

Contribution

It introduces a novel closed-form formula for k-respecting cuts and demonstrates that their sizes depend only on 2-respecting cuts, advancing graph cut analysis methods.

Findings

Closed-form formula for k-respecting cuts.

k-respecting cut sizes depend only on 2-respecting cuts.

Simplifies computation of graph cuts.

Abstract

We give a closed form formula to determine the size of a k-respecting cut. Further, we show that for any k, the size of the k-respecting cut can be found only using the size of 2-respecting cuts.