  Let $K$ be the quotient field of a discrete valuation ring $R$ with residue
characteristic $\not=2$, and let $C$ be a hyperelliptic curve over $K$. We
assume that all geometric branch points of the double covering
$C\twoheadrightarrow{\mathbb P}^1_K$ are rational and mark both $C$ and
${\mathbb P}^1_K$ with these branch points. After possibly replacing $R$ by a
ramified extension of degree $2$, we give a direct construction for the stable
model of $C$ as a marked curve over $R$. We deduce that the closed fiber of
this stable model is determined completely by the closed fiber of the stable
model of the marked ${\mathbb P}^1_K$. In particular, the dual graph and other
information for the former can be read off directly from the corresponding
information for the latter.
