A Short Proof of Tuza's Conjecture for Weak Saturation in Hypergraphs
Abstract
ABSTRACT Given an ‐uniform hypergraph and a positive integer , the weak saturation number is the minimum number of edges in an ‐uniform hypergraph on vertices such that the missing edges in can be added, one at a time, so that each added edge creates a copy of . Shapira and Tyomkyn (Proceedings of the American Mathematical Society, 2023) proved Tuza's conjecture on the asymptotic behaviour of . In this paper we provide a significantly shorter proof of the conjecture.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Tensor decomposition and applications
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Journal of Graph Theory
- Volume
- 113
- Issue
- 3
- Pages
- 523–526
- Publication date
- 10 June 2026
- Language
- EN