Fractional chromatic number of a random subgraph

It is well known that a random subgraph of the complete graph K n has chromatic number Θ ( n ∕ log n ) w.h.p. Boris Bukh asked whether the same holds for a random subgraph of any n ‐chromatic graph, at least in expectation. In this paper it is shown that for every graph, whose fractional chromatic number is at least n , the fractional chromatic number of its random subgraph is at least n ∕ ( 8 log 2 ( 4 n ) ) with probability more than 1 − 1 2 n . This gives the affirmative answer for a strengthening of Bukh's question for the fractional chromatic number.