Gašper Domen Romih - About embedding hypergraphs in ℓ_1 space

Abstract: Embeddings of finite metric spaces into well-known spaces such as hypercube, Hamming space and ℓ_1 are well studied. One such example of a finite metric space is a graph metric space. Graphs that can be isometrically embedded in the above metric spaces are well known and characterized. In this talk we will discuss some characterizations of graphs that can be embedded in a ℓ_1 space and use similar methods to study which hypergraphs can be embedded in ℓ_1 space. More specifically, we will consider partial cube hypergraphs and α-acyclic hypergraphs.