  We consider the problem of online graph colouring. Whenever a node is
requested, a colour must be assigned to the node, and this colour must be
different from the colours of any of its neighbours. According to the greedy
algorithm the node is coloured by the colour with the smallest possible $k$.
  The goal is to use as few colours as possible. We propose an algorithm, where
the node is coloured not immediately, but only after the collection of next
requests stored in the buffer of size $j$. In other words, the first node in
the buffer is coloured definitively taking into account all possible
colourisations of the remaining nodes in the buffer. If there are $r$ possible
corrected colourings, then the one with the probability $1/r$ is chosen. The
first coloured node is removed from the buffer to enable the entrance of the
next request. A number of colours in a two examples of graphs: crown graphs and
Kneser graphs have been analysed.
