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Multi-coloured Hamilton cycles in random edge-coloured graphs (2002)

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@MISC{Cooper02multi-colouredhamilton,
    author = {Colin Cooper and Alan Frieze},
    title = {Multi-coloured Hamilton cycles in random edge-coloured graphs},
    year = {2002}
}

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Abstract:

We define a space of random edge-coloured graphs n,m,n which correspond naturally to edge n-colourings of Gn,m. We show that there exist constants K0, K1 _ 21 such that provided m _ Kon log n and n _ Kin then a random edge coloured graph contains a multi-coloured Hamilton cycle with probability tending to 1, as the number of vertices n tends to infinity.

Citations

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