  Given a bounded open set $\Omega$ in $\mathbb{R}^n$ (or a compact Riemannian
manifold with boundary), and a partition of $\Omega$ by $k$ open sets
$\omega_j$, we consider the quantity $\max_j \lambda(\omega_j)$, where
$\lambda(\omega_j)$ is the ground state energy of the Dirichlet realization of
the Laplacian in $\omega_j$. We denote by $\mathfrak{L}_k(\Omega)$ the infimum
of $\max_j \lambda(\omega_j)$ over all $k$-partitions. A minimal $k$-partition
is a partition which realizes the infimum. The purpose of this paper is to
revisit properties of nodal sets and to explore if they are also true for
minimal partitions, or more generally for spectral equipartitions. We focus on
the length of the boundary set of the partition in the 2-dimensional situation.
