We deduce a generation theorem for minimal braces from McCuaig's
simple brace generation theorem. As a corollary, we obtain an upper bound of
$5n-10$ on the number of edges of a minimal brace of order $2n$, and we provide
a complete characterisation of minimal braces that achieve this upper bound. This is
joint work with Marcelo H. de Carvalho and Nishad Kothari.
Later in 2017, Kawarabayashi, Ozeki and the speaker proved a generalization of this result to other surfaces in which ``holes'' in the triangulation were allowed. However, the face-width of the embedded triangulation had to be at least $6$.
Today we present a planar analogue of this result.