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Séminaire Lotharingien de Combinatoire, B33b (1994), 20 pp.

# R. Bodendiek, R. Lang

# On Alternating Products of Graph Relations

** Abstract. **
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.

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