The t-improper chromatic number of random graphs
Combinatorics, Probability and Computing
The max quasi-independent set problem
Journal of Combinatorial Optimization
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For the Erdos-Renyi random graph G"n","p, we give a precise asymptotic formula for the size @a@?"t(G"n","p) of a largest vertex subset in G"n","p that induces a subgraph with average degree at most t, provided that p=p(n) is not too small and t=t(n) is not too large. In the case of fixed t and p, we find that this value is asymptotically almost surely concentrated on at most two explicitly given points. This generalises a result on the independence number of random graphs. For both the upper and lower bounds, we rely on large deviations inequalities for the binomial distribution.