The t-improper chromatic number of random graphs

Authors:
Ross j. Kang;Colin Mcdiarmid
Affiliations:
School of computer science, mcgill university, montréal, québec, h2a 2a7, canada (e-mail: rosskang@cs.mcgill.ca);Department of statistics, university of oxford, 1 south parks road, oxford ox1 3tg, uk (e-mail: cmcd@stats.ox.ac.uk)
Venue:
Combinatorics, Probability and Computing
Year:
2010

Citing 3
Cited 1

Generalized chromatic numbers of random graphs

SIAM Journal on Discrete Mathematics
Defective coloring revisited

Journal of Graph Theory
List Improper Colourings of Planar Graphs

Combinatorics, Probability and Computing

Largest sparse subgraphs of random graphs

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the t-improper chromatic number of the Erdős–Rényi random graph Gn,p. The t-improper chromatic number χt(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 χt(Gn,p) over the range of choices for the growth of t = t(n).