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- W2051205297 abstract "A conjecture of Erdős, Gyárfás, and Pyber says that in any edge-colouring of a complete graph with r colours, it is possible to cover all the vertices with r vertex-disjoint monochromatic cycles. So far, this conjecture has been proven only for r=2. In this paper we show that in fact this conjecture is false for all r⩾3. In contrast to this, we show that in any edge-colouring of a complete graph with three colours, it is possible to cover all the vertices with three vertex-disjoint monochromatic paths, proving a particular case of a conjecture due to Gyárfás. As an intermediate result we show that in any edge-colouring of the complete graph with the colours red and blue, it is possible to cover all the vertices with a red path, and a disjoint blue balanced complete bipartite graph." @default.
- W2051205297 created "2016-06-24" @default.
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- W2051205297 date "2014-05-01" @default.
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- W2051205297 title "Partitioning edge-coloured complete graphs into monochromatic cycles and paths" @default.
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- W2051205297 doi "https://doi.org/10.1016/j.jctb.2014.01.003" @default.
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