  The \emph{graph of irreducible parabolic subgroups} is a combinatorial object
associated to an Artin-Tits group $A$ defined so as to coincide with the curve
graph of the $(n+1)$-times punctured disk when $A$ is Artin's braid group on
$(n+1)$ strands. In this case, it is a hyperbolic graph, by the celebrated
Masur-Minsky's theorem. Hyperbolicity for more general Artin-Tits groups is an
important open question. In this paper, we give a partial affirmative answer.
  For $n\geqslant 3$, we prove that the graph of irreducible parabolic
subgroups associated to the Artin-Tits group of spherical type $B_n$ is also
isomorphic to the curve graph of the $(n+1)$-times punctured disk, hence it is
hyperbolic.
  For $n\geqslant 2$, we show that the graphs of irreducible parabolic
subgroups associated to the Artin-Tits groups of euclidean type $\widetilde
A_n$ and $\widetilde C_n$ are isomorphic to some subgraphs of the curve graph
of the $(n+2)$-times punctured disk which are not quasi-isometrically embedded.
We prove nonetheless that these graphs are hyperbolic.
