Embedding balanced image-designs into (balanced) image-designs Original Research Article

Denote by image a image-design of order image and block size k (every path has k vertices and image edges). A image having the property that every vertex meets the same number of paths [P. Hell, A. Rosa, Graph decompositions, handcuffed prisoners, and balanced image-designs, Discrete Math. 2 (1972) 229–252] is called balanced. Denote by image a balanced image. Let image, image. We say that a image image is embedded into a image image if there is an injective mapping image such that B is a subgraph of image for every image. In this paper we give the necessary and sufficient conditions for embedding balanced image-designs into (balanced) image-designs.