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."