Here is a summary of what the release tests for the CompleteStateGraph entail:

testCompleteStateGraphDuplicateCheck -- Constructs graph for 2x2 boards and verifies that there are no duplicate Nodes.
testCompleteStateGraphCompleteness -- Constructs graph for 2x2 boards and verifies that there are 29 Nodes. Also tests out your copy constructor and operator= to make sure we are getting deep copies.
testCompleteStateGraphEfficiency -- Constructs graph for 3x3 boards and verifies that there are the correct number of Nodes. If your code is inefficient you will fail the test because it will "time out".
testCompleteStateGraphMemoryLeaks -- Constructs the graph for 2x2 boards, verifies that it is the correct graph, and then destroys the graph. You will fail the test if you have memory leaks.

Note: You will fail ALL of the above tests if your BoardState::operator< is implemented incorrectly!