Year: 2024
Type: preprint
Abstract: Clustering a signed graph means partitioning the vertices into sets ("clusters") so that every positive edge, and no negative edge, is within a cluster. Clustering is not always possible; the obstruction is circles with exactly one negative edge ("weakly negative circles"). The correlation clustering problem is to cluster with the minimum number of edges that violate the clustering rule, called $Q$. A lower bound is $w$, the maximum number of edge-disjoint weakly negative circles. If every two such circles are edge disjoint, then $Q=w$. We characterize signed graphs of this kind.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4396745269