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The pants graph of a compact orientable surface S, defined by Hatcher and Thurston, is a simplicial graph associated with S. Given two pants decompositions of a compact orientable surface S, we give anÌýupper bound for their distance in the pants graph that depends logarithmically on theirÌýintersection number and polynomially on the Euler characteristic of S. As a consequence,Ìýwe find an upper bound on the volume of the convex core of a maximal cusp (which is aÌýhyperbolic structures on S ×R where given pants decompositions of the conformal boundaryÌýare pinched to annular cusps). Similarly, given two one-vertex triangulations of S, we giveÌýan upper bound for the number of flips and twist maps needed to convert one triangulationÌýinto the other. The proofs rely on using pre-triangulations, train tracks, and an algorithm ofÌýAgol, Hass, and Thurston.

This is joint work with Marc Lackenby.Ìý