Embedding products into symmetric products of finite graphs
The question treated in the paper, under the usual notation, is the embeddability of the product \(X^n\) into the symmetric product \(F_n(X)\) when \(X\) is a finite graph. It has been proved previously that if \(X\) is a finite graph, then \(X^2\) can be embedded into \(F_2(X)\) iff \(X\) is an arc. The obtained result says that the same statement holds for \(n=3\). So the following holds: If \(X\) is a finite graph, then \(X^3\) can be embedded into \(F_3(X)\) iff \(X\) is an arc. Besides some other results, at the end of the paper the authors construct a geometric model for \(F_3(Y)\), where \(Y\) is a simple triod.
scientific article; zbMATH DE number 6894000