Colour-balanced k-edge-coloured K_{2kt} has a perfect matching adjustable to colour-balance by recolouring O(k^2) edges.
On the existence of zero-sum perfect matchings of complete graphs
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Colour-balanced subgraphs
Colour-balanced k-edge-coloured K_{2kt} has a perfect matching adjustable to colour-balance by recolouring O(k^2) edges.