Cuckoo hashing is an efficient technique for creating large hash tables with
high space utilization and guaranteed constant access times. There, each item
can be placed in a location given by any one out of k different hash functions.
In this paper we investigate further the random walk heuristic for inserting in
an online fashion new items into the hash table.
We prove that there is a constant $c >0$, such that whenever $p \ge n^{-c}$,
with probability tending to 1 when $n$ goes to infinity, every maximum
triangle-free subgraph of the random graph $G_{n,p}$ is bipartite. This answers
a question of Babai, Simonovits and Spencer (Journal of Graph Theory, 1990).
We prove that there is a constant $c >0$, such that whenever $p \ge n^{-c}$,
with probability tending to 1 when $n$ goes to infinity, every maximum
triangle-free subgraph of the random graph $G_{n,p}$ is bipartite. This answers
a question of Babai, Simonovits and Spencer (Journal of Graph Theory, 1990).