TY - JOUR

T1 - Rainbow matchings and algebras of sets

AU - Nivasch, Gabriel

AU - Omri, Eran

N1 - Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/11

Y1 - 2015/11

N2 - Grinblat (2002) asks the following question in the context of algebras of sets: What is the smallest number v=v(n) such that, if A1,..., An are n equivalence relations on a common finite ground set X, such that for each i there are at least v elements of X that belong to Ai-equivalence classes of size larger than 1, then X has a rainbow matching-a set of 2n distinct elements a1, b1,..., an, bn, such that ai is Ai-equivalent to bi for each i? Grinblat has shown that v(n)≤10n/3+O(√n). He asks whether v(n)=3n-2 for all n≥. 4. In this paper we improve the upper bound (for all large enough n) to v(n)≤16n/5+O(1).

AB - Grinblat (2002) asks the following question in the context of algebras of sets: What is the smallest number v=v(n) such that, if A1,..., An are n equivalence relations on a common finite ground set X, such that for each i there are at least v elements of X that belong to Ai-equivalence classes of size larger than 1, then X has a rainbow matching-a set of 2n distinct elements a1, b1,..., an, bn, such that ai is Ai-equivalent to bi for each i? Grinblat has shown that v(n)≤10n/3+O(√n). He asks whether v(n)=3n-2 for all n≥. 4. In this paper we improve the upper bound (for all large enough n) to v(n)≤16n/5+O(1).

KW - Algebra of sets

KW - Equivalence relation

KW - Rainbow matching

UR - http://www.scopus.com/inward/record.url?scp=84947721947&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2015.06.035

DO - 10.1016/j.endm.2015.06.035

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AN - SCOPUS:84947721947

SN - 1571-0653

VL - 49

SP - 251

EP - 257

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -