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Abstract
For integers
n
>
k
> 1 let
[ n ]
k denote the collection
of all
k -subsets of the
standard
n -element
set. For
s
≥ 2 and
families
ℱ i
⊂
[ n ]
k i ,
1
≤
i
≤
s ,
( F 1 , … , F s ) is called a
rainbow
matching if
F i
∈ ℱ i
and the
F i are
pairwise disjoint. Theorem 1.5 provides the best possible upper bounds for the product of
the sizes of
ℱ i
if
n is
sufficiently large and they span no rainbow matching. For the case of graphs
( k
= 2 ) some
sharper bounds are established.
Keywords
finite sets, matchings, Erdős–Ko–Rado
Mathematical Subject Classification
Primary: 05D05
Milestones
Received: 1 February 2022
Revised: 9 June 2022
Accepted: 23 June 2022
Published: 15 October 2022