n-cube Coxeter plane projections in the Bk Coxeter groups project into k-cube graphs, with power of two vertices overlapping in the projective graphs.
The vertices of the polygon are then 3-colored in such a way that every triangle has all three colors.
Bipartite graph, a graph in which the vertices are partitioned into two sets and every edge has an endpoint in each set
The simplest algorithm to find an EMST in two dimensions, given n points, is to actually construct the complete graph on n vertices, which has n(n-1)/2 edges, compute each edge weight by finding the distance between each pair of points, and then run a standard minimum spanning tree algorithm (such as the version of Prim's algorithm or Kruskal's algorithm) on it.
The expected number of F-light edges in G is at most n/p where n is the number of vertices in G
They were formulated by Eluvathingal Devassy Jemmis to explain the structures of condensed polyhedral boranes such as B20H16, which are obtained by condensing polyhedral boranes, by sharing a triangular face, an edge, a single vertex or even four vertices.
They also show that this median of a set S of vertices in a median graph satisfies the Condorcet criterion for the winner of an election: compared to any other vertex, it is closer to a majority of the vertices in S.
However, two Hamiltonian cycles are considered to be equivalent if they connect the same vertices in the same cyclic order regardless of the starting vertex, while in the ménage problem the starting position is considered significant: if, as in Alice's tea party, all the guests shift their positions by one seat, it is considered a different seating arrangement even though it is described by the same cycle.
Alan M. Frieze showed that given a complete graph on n vertices, with edge weights that are independent identically distributed random variables with distribution function satisfying , then as n approaches +∞ the expected weight of the MST approaches , where is the Riemann zeta function.
It is also possible to formulate a version of the point set or polygon triangulation problems in which one is allowed to add Steiner points, extra vertices, in order to reduce the total edge length of the resulting triangulations.
Another possibility is the particle mesh method in which space is discretised on a mesh and, for the purposes of computing the gravitational potential, particles are assumed to be divided between the nearby vertices of the mesh.
Thus, a circle having that edge as diameter must be empty of vertices, so the Pitteway triangulation consists of the Gabriel graph together with the convex hull of the point set.
Reuleaux tetrahedron, the intersection of four spheres of equal radius centered at the vertices of a regular tetrahedron
In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope).
Planar separator theorem (graph theory) states that any planar graph can be split into smaller pieces by removing a small number of vertices.
The Fermat point of a triangle, the solution to the Steiner tree problem for the three vertices of the triangle
The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with k vertices (k is fixed).
Waaihoek is the name of a peak at one of the vertices of a very large, remote, rugged and mountainous rural property called Zuurberg ("Sour Mountain"), located about 60km north-east of Cape Town, on the margin of a great sandstone massif known as the Hex River Mountains.