The local cover

Much of my recent work has focused on the local vs. global structure of graphs. A big piece of the local-global framework I’m working with is a model of local structure called the local cover, first introduced in this paper.

The local cover is a very different way of thinking about graph structure than I had seen previously. I think it’s a unique and thought-provoking perspective, and it’s influenced some of the ways that my thoughts on graph structure have changed in the past couple of years.

I wrote a short exposition explaining the construction and some of the key ideas behind the local cover, trying to emphasize the intuition and motivation behind the concept. You can read it here. My goal is for the writeup to be an accessible introduction to the concept, and an invitation for others to think about and work with the local cover. Please email me if you have any thoughts or comments on the writeup!