Projection properties of graphs without either triangle or square
The notion of projection property, which was introduced in 1990 by \textit{E. Corominas} [C. R. Acad. Sci. Paris 311, Sér. I, 199-204 (1990)] for ordered sets, is considered by this author in the context of graphs without either triangle or square. The main result proven is stated as follows: Let \(G\) be a graph without either triangle or square. The following conditions are equivalent: (i) \(G\) verifies \(\text{PPC}_2\). (ii) \(G\) verifies \(\text{PPA}_2\). (iii) \(G\) verifies \(\text{PPA}_n\) for all \(n\). (iv) \(G\) is connected and, for every edge whose omission disconnects it, not one of the two corresponding connected components is a tree. The reader is referred to section 2 of the paper for the meaning of \(\text{PPC}_n\) (\(n\)-property of cartesian projection) and \(\text{PPA}_n\) (\(n\)-property of affine projection).
scientific article; zbMATH DE number 847627