| Abstract | : | The study of graphs as representations of certain combinatorial (or geometric) incidence (or intersection) structures has a long and rich history. One particular variant is the following: for a given graph G, we say that it admits a path-representation in H if there are edge-disjoint paths in a graph H that correspond to the vertices of G with incidence if and only if the corresponding paths intersect. We consider a natural extremal parameter prn(G) arising from such representations, and study this related parameter for certain families including cliques, trees, and G(n, p) for constant p. This is based on joint work with Shagnik Das, Brahadeesh Sankarnarayanan, and Umesh Shankar. |
