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Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

The intersection number omega(G) of a given graph G is the minimum number of elements in a set S such that G is an intersection graph on S.

A 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

The Miquel configuration is the 6_4 configuration illustrated above. Its Levi graph is the rhombic dodecahedral graph.

A graph H is called a topological minor, also known as a homeomorphic subgraph, of a graph G if a graph subdivision of H is isomorphic to a subgraph of G. Every topological ...

An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each ...

An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...

A generalized dodecagon is a generalized polygon of order 12. GD(1,2) is the (3,12)-cage graph, more commonly known as the Tutte 12-cage. GD(2,1) is the line graph of the ...