Year: 2026
Type: preprint
Abstract: Let $λ$ be the minimum cut value of an $n$-vertex undirected multigraph. For every fixed $α>1$, we prove that there are $O(n^{\lceil2α\rceil-1})$ cuts of size strictly below $αλ$. The exponent is sharp. The proof combines splitting off and sampling with a bound on the size of nested families of vertex sets.
Source: arXiv (Cornell University)
Authors: Xu, Chao, Yang, Mingdong
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212137170