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In 1978, Richard Rado showed that every edge-coloured complete graph ofcountably infinite order can be partitioned into monochromatic paths ofdifferent colours. He asked whether this remains true for uncountable completegraphs and a notion of \emph{generalised paths}. In 2016, Daniel Soukupanswered this in the affirmative and conjectured that a similar result shouldhold for complete bipartite graphs with bipartition classes of the sameinfinite cardinality, namely that every such graph edge-coloured with $r$colours can be partitioned into $2r-1$ monochromatic generalised paths witheach colour being used at most twice.  In the present paper, we give an affirmative answer to Soukup's conjecture.

Partitioning edge-coloured infinite complete bipartite graphs into monochromatic paths