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Partitioning edge-coloured infinite complete bipartite graphs into monochromatic paths

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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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References

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Authors and Affiliations

  1. Department of Mathematics, University of Hamburg, Bundesstraße 55 (Geomatikum), 20146, Hamburg, Germany

    Carl Bürger & Max Pitz

Authors
  1. Carl Bürger
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  2. Max Pitz
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Correspondence to Carl Bürger.

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Bürger, C., Pitz, M. Partitioning edge-coloured infinite complete bipartite graphs into monochromatic paths. Isr. J. Math. 238, 479–500 (2020). https://doi.org/10.1007/s11856-020-2030-z

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  • DOI: https://doi.org/10.1007/s11856-020-2030-z

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