A combinatorial map is a combinatorial representation of a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding, a rotation system, an orientable ribbon graph, a fat graph, or a cyclic graph.[1] More generally, an -dimensional combinatorial map
is a combinatorial representation of a graph on an -dimensional orientable manifold.
Combinatorial maps are used as efficient data structures in image representation and processing, in geometrical modeling. This model is related to simplicial complexes and to combinatorial topology. A combinatorial map is a boundary representation model; it represents object by its boundaries.
^Cite error: The named reference br01 was invoked but never defined (see the help page).
A combinatorialmap is a combinatorial representation of a graph on an orientable surface. A combinatorialmap may also be called a combinatorial embedding...
means of stereographic projection. Plane graphs can be encoded by combinatorialmaps or rotation systems. An equivalence class of topologically equivalent...
of here as a 1-dimensional cell complex) a combinatorialmap is a continuous map f : Γ → Γ such that: The map f takes vertices to vertices. For every edge...
generalized map is a topological model which allows one to represent and to handle subdivided objects. This model was defined starting from combinatorialmaps in...
In combinatorial mathematics, rotation systems (also called combinatorial embeddings or combinatorialmaps) encode embeddings of graphs onto orientable...
theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions...
complexity. Quad-edge data structure Doubly linked face list Winged edge Combinatorialmap Muller, D. E.; Preparata, F. P. (1978). "Finding the Intersection...
the term combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial identity is...
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric...
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures...
In mathematics, and in particular in combinatorics, the combinatorial number system of degree k (for some positive integer k), also referred to as combinadics...
cartogram (also called a value-area map or an anamorphic map, the latter common among German-speakers) is a thematic map of a set of features (countries,...
model constructed by planar surfaces only Bezier curve Bezier surface Combinatorialmaps Coons surface Function representation Geometric modeling kernel NURBS...
The multidimensional assignment problem (MAP) is a fundamental combinatorial optimization problem which was introduced by William Pierskalla. This problem...
exactly when the subdivision rule is conformal, as described in the combinatorial Riemann mapping theorem. Applications of subdivision rules. Islamic...
Edge *edge; } class Face { Edge *edge; } Quad-edge data structure Combinatorialmaps Doubly connected edge list Doubly linked face list Half-edge data...
In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of...
In algebra, an additive map, Z {\displaystyle Z} -linear map or additive function is a function f {\displaystyle f} that preserves the addition operation:...
between which the chess king can move. Map graphs can be represented combinatorially as the "half-squares of planar bipartite graphs". That is, let G =...
Because there are a limited number of spectrally distinct fluorophores, a combinatorial labeling method is used to generate many different colors. Fluorophore...
the simplicial set. Indeed, one may view a simplicial set as a purely combinatorial construction designed to capture the essence of a "well-behaved" topological...
retains a combinatorial nature that allows for computation (often with a much smaller complex). An older name for the subject was combinatorial topology...
(2004), "Graphs and digraphs with all 2-factors isomorphic", Journal of Combinatorial Theory, Series B, 92 (2): 395–404, doi:10.1016/j.jctb.2004.09.004, MR 2099150...
In the mathematics of combinatorial games, the sum or disjunctive sum of two games is a game in which the two games are played in parallel, with each...
from which set elements are taken. It relies on existing non-adaptive combinatorial group testing scheme by Eppstein, Goodrich and Hirschberg. Unlike the...
exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations...
Global Information