@inproceedings{brun-99-2,



AUTHOR = {L. {B}run and {K}ropatsch, Walter},
TITLE = {Dual Contraction of Combinatorial Maps},
BOOKTITLE = {$2^{nd}$ IAPR-TC-15 Workshop on Graph-based Representations},
EDITOR = {{Kropatsch},Walter and
{{J}olion}, J.-M.},
PUBLISHER = {{"O}sterreichische Computer Gesellschaft},
VOLUME = {126},
ADDRESS = {Haindorf, Austria},
YEAR = {1999},
MONTH = {May},
PAGES = {145-154},
theme = {hierarchical},
url = {slides:=https://brunl01.users.greyc.fr/ARTICLES/slides_cvww1999.ps},
abstract = "This paper presents a new formalism for
irregular graph pyramids based on
combinatorial maps. Such pyramids consist of
a stack of successively reduced graphs. Each
smaller graph is derived from the larger one
in the stack by a graph transformation called
dual graph contraction. The basic operations
of this transformation are contraction and
removal of edges. In this paper these two
basic operations are translated into the
formalism of combinatorial maps and should
enable the construction of combinatorial
pyramids. A combinatorial map encodes a
planar graph by two permutations encoding the
edges and their orientation around the
vertices. Combining the useful properties of
irregular pyramids offers a potential
alternative for representing structures at
multiple levels of abstraction."

 }