A new algorithm for reducing the bandwidth and profile of a sparse matrix is described. Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill-McKee algorithm, yet requires significantly less computation time.

The conjecture that for all sufficiently large p any tournament of order p is uniquely reconstructable from its point-deleted subtournaments is shown to be false. Counterexamples are presented for all orders of the form 2" + 1 and 2" + 2. The largest previously known counterexamples were of order 8.

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