Search results
Results from the WOW.Com Content Network
A planar graph is said to be convex if all of its faces (including the outer face) are convex polygons. Not all planar graphs have a convex embedding (e.g. the complete bipartite graph K 2,4). A sufficient condition that a graph can be drawn convexly is that it is a subdivision of a 3-vertex-connected planar graph.
Pages in category "Planar graphs" The following 88 pages are in this category, out of 88 total. This list may not reflect recent changes. ...
A 1-planar graph is said to be an optimal 1-planar graph if it has exactly 4n − 8 edges, the maximum possible. In a 1-planar embedding of an optimal 1-planar graph, the uncrossed edges necessarily form a quadrangulation (a polyhedral graph in which every face is a quadrilateral). Every quadrangulation gives rise to an optimal 1-planar graph ...
An outer-1-planar graph, analogously to 1-planar graphs can be drawn in a disk, with the vertices on the boundary of the disk, and with at most one crossing per edge. Every maximal outerplanar graph is a chordal graph. Every maximal outerplanar graph is the visibility graph of a simple polygon. [17]
The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
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.
In Vizing's planar graph conjecture, Vizing (1965) states that all simple, planar graphs with maximum degree six or seven are of class one, closing the remaining possible cases. Independently, Zhang (2000) and Sanders & Zhao (2001) partially proved Vizing's planar graph conjecture by showing that all planar graphs with maximum degree seven are ...
In an n-vertex connected graph, the largest planar subgraph has at most 3n − 6 edges, and any spanning tree forms a planar subgraph with n − 1 edges. Thus, it is easy to approximate the maximum planar subgraph within an approximation ratio of one-third, simply by finding a spanning tree.