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.

The following versions are available: