Open Access
3- https://doi.org/10.1017/s0963548318000147
A Stability Theorem for Matchings in Tripartite 3-Graphs
- Apr 2, 2018
- Combinatorics, Probability and Computing
- Penny Haxell +1 more
Abstract
It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + ϵ)n/2 is close in structure to the extremal configuration, where ‘closeness’ is measured by an explicit function of ϵ.
- # Matching Number
- # Extremal Configuration
- # Tripartite Hypergraph
- # Explicit Function
- # Stability Theorem
