We define in this paper several Hopf algebras describing the combinatorics of
the so-called multi-scale renormalization in quantum field theory. After a
brief recall of the main mathematical features of multi-scale renormalization,
we define assigned graphs, that are graphs with appropriate decorations for the
multi-scale framework. We then define Hopf algebras on these assigned graphs
and on the Gallavotti-Nicol\`o trees, particular class of trees encoding the
supplementary informations of the assigned graphs. Several morphisms between
these combinatorial Hopf algebras and the Connes-Kreimer algebra are given.
Finally, scale dependent couplings are analyzed via this combinatorial
algebraic setting.Comment: 26 pages, 3 figures; the presentation of the results has been
reorganized. Several details of various proofs are given and some references
have been adde
