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Rooted kernels and Labeled Combinatorial Pyramids

Jocelyn Marchadier &
Luc Brun &
Walter G. Kropatsch.
An irregular pyramid consists of a stack of
successively reduced graphs. Each smaller graph is deduced
from the preceding one using contraction or removal kernels. A
contraction (resp. removal) kernel defines a forest of the
initial (resp. dual ) graph, each tree of this forest being
reduced to a single vertex (resp. dual vertex) in the reduced
graph. A combinatorial map encodes a planar graph thanks to
two permutations encoding the edges and their orientation
around the vertices. We present in this article a new
definition of contraction and removal kernels which allows to
encode the different values attached to a given vertex, dual
vertex or edge along the pyramid.