A Rainbow r-Partite Version of the Erdős-Ko-Rado Theorem
نویسندگان
چکیده
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, i.e. a choice of disjoint edges fi ∈ Fi. We prove this conjecture for r = 2 and r = 3.
منابع مشابه
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 26 شماره
صفحات -
تاریخ انتشار 2017