A Rainbow r-Partite Version of the Erdős–Ko–Rado Theorem
2017 ◽
Vol 26
(3)
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pp. 321-337
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Keyword(s):
Let [n]r be the complete r-partite hypergraph with vertex classes of size n. It is an easy exercise to show that every set of more than (k−1)nr−1 edges in [n]r contains a matching of size k. We conjecture the following rainbow version of this observation: if F1,F2,. . .,Fk ⊆ [n]r are of size larger than (k−1)nr−1 then there exists a rainbow matching, that is, a choice of disjoint edges fi ∈ Fi. We prove this conjecture for r=2 and r=3.
2014 ◽
Vol 38
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pp. 97-101
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Keyword(s):
2018 ◽
Vol 10
(02)
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pp. 1850021
Keyword(s):
Keyword(s):