Listing Triconnected Rooted Plane Graphs
نویسندگان
چکیده
A plane graph is a drawing of a planar graph in the plane such that no two edges cross each other. A rooted plane graph has a designated outer vertex. For given positive integers n ≥ 1 and g ≥ 3, let G3(n, g) denote the set of all triconnected rooted plane graphs with exactly n vertices such that the size of each inner face is at most g. In this paper, we give an algorithm that enumerates all plane graphs in G3(n, g). The algorithm runs in constant time per each by outputting the difference from the previous output.
منابع مشابه
Generating Internally Triconnected Rooted Graphs
A biconnected plane graph G is called internally triconnected if any cut-pair consists of outer vertices and its removal results in only components each of which contains at least one outer vertex. In a rooted plane graph, an edge is designated as an outer edge with a specified direction. For given positive integers n ≥ 1 and g ≥ 3, let G3(n, g) (resp., Gint(n, g)) denote the class of all trico...
متن کاملListing All Plane Graphs
In this paper we give a simple algorithm to generate all connected rooted plane graphs with at most m edges. A “rooted” plane graph is a plane graph with one designated (directed) edge on the outer face. The algorithm uses O(m) space and generates such graphs in O(1) time per graph on average without duplications. The algorithm does not output the entire graph but the difference from the previo...
متن کاملGenerating All Triangulations of Plane Graphs
In this paper, we deal with the problem of generating all triangulations of plane graphs. We give an algorithm for generating all triangulations of a triconnected plane graph G of n vertices. Our algorithm establishes a tree structure among the triangulations of G, called the “tree of triangulations,” and generates each triangulation of G in O(1) time. The algorithm uses O(n) space and generate...
متن کاملConvex Grid Drawings of Plane Graphs with Rectangular Contours
In a convex drawing of a plane graph, all edges are drawn as straightline segments without any edge-intersection and all facial cycles are drawn as convex polygons. In a convex grid drawing, all vertices are put on grid points. A plane graph G has a convex drawing if and only if G is internally triconnected, and an internally triconnected plane graph G has a convex grid drawing on an (n− 1)× (n...
متن کاملSquare-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interiordisjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points. We characterize the partial ...
متن کامل