Rainbow $H$-Factors of Complete $s$-Uniform $r$-Partite Hypergraphs
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We say a $s$-uniform $r$-partite hypergraph is complete, if it has a vertex partition $\{V_1,V_2,...,V_r\}$ of $r$ classes and its hyperedge set consists of all the $s$-subsets of its vertex set which have at most one vertex in each vertex class. We denote the complete $s$-uniform $r$-partite hypergraph with $k$ vertices in each vertex class by ${\cal T}_{s,r}(k)$. In this paper we prove that if $h,\ r$ and $s$ are positive integers with $2\leq s\leq r\leq h$ then there exists a constant $k=k(h,r,s)$ so that if $H$ is an $s$-uniform hypergraph with $h$ vertices and chromatic number $\chi(H)=r$ then any proper edge coloring of ${\cal T}_{s,r}(k)$ has a rainbow $H$-factor.
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2013 ◽
Vol 333-335
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pp. 1452-1455
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2018 ◽
Vol 10
(02)
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pp. 1850017
2015 ◽
Vol 07
(04)
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pp. 1550044
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2017 ◽
Vol 9
(1)
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pp. 37
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2012 ◽
Vol 04
(04)
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pp. 1250047
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