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Abstract
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Let
denote the maximum size of a family of subsets of an
-set
without
pairwise disjoint members. The problem of determining
was raised
by Erdős more than half a century ago. Nevertheless except for the residue classes
the exact value of
is largely unknown. In the
present paper
is determined
for most values of
(see Theorems 1.8 and 1.9). The extremal families are so-called
threshold families (see
Definition 1.4).
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Keywords
finite sets, matchings, threshold families
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Mathematical Subject Classification
Primary: 05D05
Secondary: 05C35
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Milestones
Received: 8 March 2023
Accepted: 23 August 2023
Published: 23 September 2023
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