  A graph is (m, k)-colourable if its vertices can be coloured with m colours
such that the maximum degree of any subgraph induced on ver- tices receiving
the same colour is at most k. The k-defective chromatic number for a graph is
the least positive integer m for which the graph is (m, k)-colourable. All
triangle-free graphs on 8 or fewer vertices are (2, 1)-colourable. There are
exactly four triangle-free graphs of order 9 which have 1-defective chromatic
number 3. We show that these four graphs appear as subgraphs in almost all
triangle-free graphs of order 10 with 1-defective chromatic number equal to 3.
In fact there is a unique triangle-free (3, 1)-critical graph on 10 vertices
and we exhibit this graph.
