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A Rainbow r-Partite Version of the Erdős–Ko–Rado Theorem

Part of: Extremal combinatorics

Published online by Cambridge University Press:  23 January 2017

RON AHARONI  and
DAVID HOWARD
RON AHARONI
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel (e-mail: raharoni@gmail.com)
DAVID HOWARD
Affiliation:
Department of Mathematics, Colgate University, 13 Oak Drive, Hamilton, NY 13346, USA (e-mail: dmhoward@colgate.edu)
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Abstract

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.

MSC classification

Primary: 05D05: Extremal set theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 3 , May 2017 , pp. 321 - 337
Copyright
Copyright © Cambridge University Press 2017 

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