  A signed graph is a simple graph with two types of edges: positive and
negative edges. Switching a vertex $v$ of a signed graph corresponds to
changing the type of each edge incident to $v$.
  A homomorphism from a signed graph $G$ to another signed graph $H$ is a
mapping $\varphi: V(G) \rightarrow V(H)$ such that, after switching some of the
vertices of $G$, $\varphi$ maps every edge of $G$ to an edge of $H$ of the same
type. The chromatic number $\chi_s(G)$ of a signed graph $G$ is the order of a
smallest signed graph $H$ such that there is a homomorphism from $G$ to $H$.
  The maximum average degree $mad(G)$ of a graph $G$ is the maximum of the
average degrees of all the subgraphs of $G$. We denote $\mathcal{M}_k$ the
class of signed graphs with maximum average degree less than $k$ and
$\mathcal{P}_g$ the class of planar signed graphs with girth at least $g$.
  We prove:
  $\chi_s(\mathcal{M}_{\frac{8}{3}}) = 4$ which implies
$\chi_s(\mathcal{P}_{8}) = 4$,
  $\chi_s(\mathcal{P}_{7}) \le 5$,
  $\chi_s(\mathcal{M}_{\frac{17}{5}}) \le 10$ which implies
$\chi_s(\mathcal{P}_{5}) \le 10$,
  $\chi_s(\mathcal{M}_{4-\frac{8}{q+3}}) \le q+1$ with $q$ a prime power
congruent to 1 modulo 4.
