First published in 1993, this thesis is concerned with the design
of efficient algorithms for listing combinatorial structures. The
research described here gives some answers to the following
questions: which families of combinatorial structures have fast
computer algorithms for listing their members? What general methods
are useful for listing combinatorial structures? How can these be
applied to those families which are of interest to theoretical
computer scientists and combinatorialists? Amongst those families
considered are unlabelled graphs, first order one properties,
Hamiltonian graphs, graphs with cliques of specified order, and
k-colourable graphs. Some related work is also included, which
compares the listing problem with the difficulty of solving the
existence problem, the construction problem, the random sampling
problem, and the counting problem. In particular, the difficulty of
evaluating Polya's cycle polynomial is demonstrated.
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