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/* Remarks */
If the class sizes are ''almost equal'' (that is <math>|n_i-n_j|\le 1</math> for every <math>1\le i<j\le k</math>) then the answer to the above question is always YES by
the skew-supermodular variant<ref name="BeKi"/> of Schrijver's [[Supermodular colouring theorem]]. A special case of the problem is the following: given a bipartite graph ''G=(A,B,E)'' with <math> d_G(v)\le k</math> for every <math>v\in A\cup B</math>, and ''k'' nonnegative integers <math>n_1,n_2,\dots,n_k</math> satisfying <math>n_1+n_2+\dots+n_k = |E|</math>. Does there exist ''k'' disjoint matchings <math>M_1,M_2,\dots,M_k\subseteq E</math> such that <math>|M_i| = n_i</math> for every ''i=1,...,k''?
A special case of the problem above is the following: given a bipartite graph ''G=(A,B,E)'' with <math> d_G(v)\le k</math> for every <math>v\in A\cup B</math>, and ''k'' nonnegative integers <math>n_1,n_2,\dots,n_k</math> satisfying <math>n_1+n_2+\dots+n_k = |E|</math>. Does there exist ''k'' disjoint matchings <math>M_1,M_2,\dots,M_k\subseteq E</math> such that <math>|M_i| = n_i</math> for every ''i=1,...,k''?
==References==
