  We present a simplified formulation of open intersection numbers, as an
alternative to the theory initiated by Pandharipande, Solomon and Tessler. The
relevant moduli spaces consist of Riemann surfaces (either with or without
boundary) with only interior marked points. These spaces have a combinatorial
description using a generalization of ribbon graphs, with a straightforward
compactification and corresponding intersection theory. Crucially, the
generating functions for the two different constructions of open intersection
numbers are identical. In particular, our construction provides a complete
proof of the statement that this generating function is a solution of the MKP
hierarchy, satisfies W-constraints, and additionally proves in the affirmative
the Q-grading conjecture for distinguishing contributions from surfaces with
different numbers of boundary components, as was previously proposed by the
author.
