Séminaire Lotharingien de Combinatoire, B33b (1994), 20 pp.
R. Bodendiek, R. Lang
On Alternating Products of Graph Relations
It is well-known that one can give an elegant version of the
Kuratowski-type theorem for the projective plane by means
of the five elementary relations R(i), i= 0,1, ... ,4, on the set
of all finite, undirected graphs without loops and multiple edges.
Furthermore, these five relations play an interesting role in
didactics of mathematics.
Following a theory given in a paper by Sawada, they have been investigated
by C. Thies.
In order to show that R(0), R(1), ..., R(4) are an appropriate
curriculum he has to deal with certain alternating products in the R(i)'s.
Here, it is shown that, in case of i=0, there exists exactly one
alternating product in the set of all alternating products of
R(0), in case of i=3 and i=4 the sets of all alternating
products of R(3) and R(4) are infinite sets.
The following versions are available: