Embedding path designs into kite systems Original Research Article

Let D be the triangle with an attached edge (i.e. D is the “kite”, a graph having vertices image and edges image, image, image, image). Bermond and Schönheim [G-decomposition of image, where G has four vertices or less, Discrete Math. 19 (1977) 113–120] proved that a kite-design of order n exists if and only if image. Let image be a nontrivial kite-design of order image, and let image with image. A path design image of order image and block size s is embedded into image if there is an injective mapping image such that B is an induced subgraph of image for every image. For each image, we determine the spectrum of all integers image such that there is a nontrivial path design of order image and block size 3 embedded into a kite-design of order n.