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- W2154503116 abstract "We present a full analysis of the expected number of 'rigid' 3-colourings of a sparse random graph. This shows that, if the average degree is at least 4.99, then as n → ∞ the expected number of such colourings tends to 0 and so the probability that the graph is 3-colourable tends to 0. (This result is tight, in that with average degree 4.989 the expected number tends to ∞.) This bound appears independently in Kaporis textitet al. [Kap]. We then give a minor improvement, showing that the probability that the graph is 3-colourable tends to 0 if the average degree is at least 4.989." @default.
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- W2154503116 date "2002-01-01" @default.
- W2154503116 modified "2023-10-18" @default.
- W2154503116 title "Upper bounds on the non-3-colourability threshold of random graphs" @default.
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- W2154503116 doi "https://doi.org/10.46298/dmtcs.299" @default.
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