- Abstract:
- We consider the $t$-improper chromatic number of the Erd{\H o}s-R{\'e}nyi random graph $G(n,p)$. The t-improper chromatic number $\chi^t(G)$ 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 $\chi^t(G(n,p))$ over the range of choices for the growth of $t = t(n)$.
- Publisher copy:
- 10.1017/S0963548309990216
-
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- Journal:
- Combin. Probab. Comput. 19 (2010), 87-98
- Volume:
- 19
- Issue:
- SPEC. ISS.
- Pages:
- 87-98
- Publication date:
- 2008-09-26
- DOI:
- EISSN:
-
1571-0653
- ISSN:
-
1571-0653
- URN:
-
uuid:4837fb8d-c30a-4a88-96a0-fb2993fee6a8
- Source identifiers:
-
97474
- Local pid:
- pubs:97474
- Language:
- English
- Keywords:
- Copyright date:
- 2008
- Notes:
- 12 pages
Journal article
The t-improper chromatic number of random graphs
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