Abstract
In 1978, Richard Rado showed that every edge-coloured complete graph of countably infinite order can be partitioned into monochromatic paths of different colours. He asked whether this remains true for uncountable complete graphs and a notion of generalised paths. In 2016, Daniel Soukup answered this in the affirmative and conjectured that a similar result should hold for complete bipartite graphs with bipartition classes of the same infinite cardinality, namely that every such graph edge-coloured with r colours can be partitioned into 2r — 1 monochromatic generalised paths with each colour being used at most twice.In the present paper, we give an affirmative answer to Soukup’s conjecture.
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