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A 1-planar graph is a graph that may be drawn in the plane with at most one simple crossing per edge, and a k-planar graph is a graph that may be drawn with at most k simple crossings per edge. A map graph is a graph formed from a set of finitely many simply-connected interior-disjoint regions in the plane by connecting two regions when they ...
Let G be a simple plane graph with n vertices; we may add edges if necessary so that G is a maximally plane graph. If n < 3, the result is trivial. If n ≥ 3, then all faces of G must be triangles, as we could add an edge into any face with more sides while preserving planarity, contradicting the assumption of maximal planarity.
In computational geometry and geometric graph theory, a planar straight-line graph (or straight-line plane graph, or plane straight-line graph), in short PSLG, is an embedding of a planar graph in the plane such that its edges are mapped into straight-line segments. [1] Fáry's theorem (1948) states that every planar graph has this kind of ...
Download as PDF; Printable version; In other projects Wikidata item; ... Visual Dictionary of Special Plane Curves This page was last edited on 24 July 2024, at 01:55 ...
A planar graph is a graph that can be drawn without crossings in the Euclidean plane.If the points belonging to vertices and edges are removed from the plane, the connected components of the remaining points form polygons, called faces, including an unbounded face extending to infinity.
Convex and strictly convex grid drawings of the same graph. In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.
A subdivision of a graph is a graph formed by subdividing its edges into paths of one or more edges. Kuratowski's theorem states that a finite graph G {\displaystyle G} is planar if it is not possible to subdivide the edges of K 5 {\displaystyle K_{5}} or K 3 , 3 {\displaystyle K_{3,3}} , and then possibly add additional edges and vertices, to ...
According to the four-color theorem, every graph that can be drawn in the plane without edge crossings can have its vertices colored using at most four different colors, so that the two endpoints of every edge have different colors, but according to Grötzsch's theorem only three colors are needed for planar graphs that do not contain three ...