Let $R$ be a complete discrete valuation ring with field of fractions $K$ and algebraically closed residue field $k$, and let $X$ be a proper, smooth, geometrically connected curve over $K$. Take a finite extension $L/K$ and a regular proper model $\widetilde{X}$ of $X$ over the ring of integers of $L$ whose special fibre $\widetilde X_k$ is semi-stable. Let $e$ be the ramification index of $L/K$. The reduction graph of $X$ is a metrised graph obtained as follows. Take a set of intervals of lengh $1/e$ indexed by the singular points of $\widetilde X_k$. For every singular point $x$ of $\widetilde X_k$, label the endpoints of the corresponding edge by the two irreducible components (possibly the same) on which $x$ lies. For every irreducible component $C$ of $\widetilde X_k$, identify all the endpoints labelled $C$. The result (as a metric space) is independent of the choice of $L$.

**Question:** Suppose we have a regular proper model of $X$ over $R$ whose special fibre $X_k$ is reduced, but not necessarily semi-stable. Suppose furthermore that we know the irreducible components and singular points of $X_k$ and their intersection multiplicities in this model. What can be said about the reduction graph of $X$?

It seems reasonable to ask this question in this generality, but I am actually interested in the modular curves X_{1}(*n*) over W_{p}[*ζ*_{p2}], where *p* is a prime number dividing *n* exactly twice and W_{p} is the ring of Witt vectors of an algebraic closure of **F**_{p}. In this situation non-semi-stable models as above were found by Katz and Mazur. What I would like specifically is an upper bound on the diameter of the reduction graph for these curves.