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Abstract
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For integers
let
denote the collection
of all
-subsets of the
standard
-element
set. For
and
families
,
,
is called a
rainbow
matching if
and the
are
pairwise disjoint. Theorem 1.5 provides the best possible upper bounds for the product of
the sizes of
if
is
sufficiently large and they span no rainbow matching. For the case of graphs
some
sharper bounds are established.
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Keywords
finite sets, matchings, Erdős–Ko–Rado
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Mathematical Subject Classification
Primary: 05D05
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Milestones
Received: 1 February 2022
Revised: 9 June 2022
Accepted: 23 June 2022
Published: 15 October 2022
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