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Colouring random subgraphs
Part of:
Graph theory
Published online by Cambridge University Press: 28 April 2025
Abstract
We study several basic problems about colouring the 
$p$-random subgraph 
$G_p$ of an arbitrary graph 
$G$, focusing primarily on the chromatic number and colouring number of 
$G_p$. In particular, we show that there exist infinitely many 
$k$-regular graphs 
$G$ for which the colouring number (i.e., degeneracy) of 
$G_{1/2}$ is at most 
$k/3 + o(k)$ with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least 
$k/2 - o(k)$.
MSC classification
Primary:
05C80: Random graphs
Secondary:
05C15: Coloring of graphs and hypergraphs
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- © The Author(s), 2025. Published by Cambridge University Press
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