This is a guide to the material contained in
an exact copy of the files formerly located on a now defunct
anonymous ftp server.
It falls naturally into two parts, Reducibility and Discharging.
Common to both parts is the file
unavoidable.conf, a list of the 633 unavoidable configurations
stored in the following format:
Vertices 1,...,r are the ring vertices (in order),
and so the configuration itself consists of vertices r + 1,
r + 2, ... n .
The set is also available in a
- N; a character string identifying the configuration;
- n r a b; where
- n is the number of vertices of the free completion;
- r is the ring-size;
- a is the cardinality of C ; and
- b is the cardinality of C' (see discussion
before (3.2) in the paper);
- k [2*k integers]; k is the number of edges in X, each edge being
represented as a pair of integers;
- the adjacency list of the free completion in a standard form
(the second column contains
the degrees in the free completion);
- coordinates of vertices of the free completion;
the i-th entry in the coordinate list is 1024 x + y where [x,y] are the coordinates
of vertex i, (0 < = x,y < 1024) .
unavoidable.conf, described above.
discharge.c, the program that verifies that the files
describe correct unavoidability proofs.
discharge.tex, documentation for the above program.
rules, the list of the discharging rules in a machine readable form.
They are also available in
discharge.pas, a Pascal version of the discharging program, written
Christopher Carl Heckman.