Efficient proper embedding of a daisy cubeVesel, Aleksander (Avtor) daisy cubepartial cubeisometric embeddingproper embeddingFor a set ▫$X$▫ of binary words of length ▫$h$▫ the daisy cube ▫$Q_h(X)$▫ is defined as the subgraph of the hypercube ▫$Q_h$▫ induced by the set of all vertices on shortest paths that connect vertices of ▫$X$▫ with the vertex ▫$0^h$▫. A vertex in the intersection of all of these paths is a minimal vertex of a daisy cube. A graph ▫$G$▫ isomorphic to a daisy cube admits several isometric embeddings into a hypercube. We show that an isometric embedding is proper if and only if the label ▫$0^h$▫ is assigned to a minimal vertex of ▫$G$▫. This result allows us to devise an algorithm which finds a proper embedding of a graph isomorphic to a daisy cube into a hypercube in linear time.Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije20212024-11-08 03:07:20Znanstveno delo91119sl