[HTML][HTML] On the maximum number of edges in a hypergraph with a unique perfect matching
… A perfect matching in H is a collection of edges { M 1 , M 2 , … , M m } ⊆ E such that M i
∩ M j = 0̸ for all i ≠ j and ⋃ i M i = V . In this note we are interested in the maximum
number of edges of a hypergraph H with a unique perfect matching. Hetyei observed (see,
eg, [1], [2], [3]) that for ordinary graphs (ie k = 2 ), this number cannot exceed m 2 . To see
this, note that at most two …
∩ M j = 0̸ for all i ≠ j and ⋃ i M i = V . In this note we are interested in the maximum
number of edges of a hypergraph H with a unique perfect matching. Hetyei observed (see,
eg, [1], [2], [3]) that for ordinary graphs (ie k = 2 ), this number cannot exceed m 2 . To see
this, note that at most two …
In this note, we determine the maximum number of edges of a k-uniform hypergraph, k≥3, with a unique perfect matching. This settles a conjecture proposed by Snevily.
Elsevier
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