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Let m, n, r, s be nonnegative integers such that n m=3r+s and 1 s 3. Let \ (n, r, s) =\array{ll n²- (n-r) ² &if\ s=1, \\[5pt n²- (n-r+1) (n-r-1) &if\ s=2, \\5pt n² - (n-r) (n-r-1) &if\ s=3. array. \] We show that there exists a constant n₀ > 0 such that if F₁, , Fₙ are 3-partite 3-graphs with n n₀ vertices in each partition class and minimum vertex degree of Fᵢ is at least (n, r, s) +1 for i n then \F₁, , Fₙ\ admits a rainbow perfect matching. This generalizes a result of Lo and Markstr\"om on the vertex degree threshold for the existence of perfect matchings in 3-partite 3-graphs. In this proof, we use a fractional rainbow matching theory obtained by Aharoni et al. to find edge-disjoint fractional perfect matching.
Lu et al. (Fri,) studied this question.