We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.
"Convexity of strata in diagonal pants graphs of surfaces." Publ. Mat. 57 (1) 219 - 237, 2013.