On the Maximum Number of Edges in a Hypergraph with a Unique Perfect Matching
Deepak Bal, Andrzej Dudek, Zelealem B. Yilma
TL;DR
This paper determines the maximum number of edges in a k-uniform hypergraph with a unique perfect matching, settling a conjecture and advancing understanding of hypergraph matchings.
Contribution
It provides a definitive answer to the maximum edge count in hypergraphs with a unique perfect matching, confirming a longstanding conjecture.
Findings
Maximum edges in k-uniform hypergraphs with unique perfect matching established
Conjecture by Snevily confirmed
Theoretical bounds derived for hypergraph structures
Abstract
In this note, we determine the maximum number of edges of a -uniform hypergraph, , with a unique perfect matching. This settles a conjecture proposed by Snevily.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Advanced Graph Theory Research