On colored designs. I
A graph \(G=(V,E)\) is said to have an \(H\)-decomposition if \(E\) is partitioned into \(E_1,E_2,\dots,E_k\) such that the edge-induced subgraphs \(G[E_i]\), \(i=1,2,\dots,k\), are all isomorphic to \(H\). The set \(\{E_i\mid 1\leq i\leq k\}\) is called an \(H\)-design for \(G\). In this paper, the problem of whether or not the existence of an \(H\)-design for a graph implies the existence of the corresponding colored designs is solved for small graphs \(H\) in the case of two or three edge colors.
scientific article; zbMATH DE number 1019053