ABSTRACT
We continue our investigation of hypercubes, which were introduced in Chapter 2. Hypercubes have numerous applications, for example in coding theory (where Gray codes are Hamilton cycles in hypercubes), computer architecture, mathematical chemistry, and phylogenetics. Hypercubes and their subgraphs are the main topic of interest not only in this chapter, but also in Chapters 18, 19, and 21. Here we introduce isometric subgraphs of hypercubes, known as partial cubes, and then continue with median graphs as retracts of hypercubes and generalizations of trees.
