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arXiv · 0809.4726

The t-improper chromatic number of random graphs

Ross J. Kang·Colin McDiarmid
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Abstract

We consider the $t$-improper chromatic number of the Erd{\H o}s-R{é}nyi random graph $G(n,p)$. The t-improper chromatic number $χ^t(G)$ of $G$ is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most $t$. If $t = 0$, then this is the usual notion of proper colouring. When the edge probability $p$ is constant, we provide a detailed description of the asymptotic behaviour of $χ^t(G(n,p))$ over the range of choices for the growth of $t = t(n)$.

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Ross J. Kang, Colin McDiarmid. 2009-04-16. The t-improper chromatic number of random graphs. https://doi.org/10.1017/s0963548309990216

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