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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).

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 ...

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 ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

A number of attractive 6-compounds of the regular dodecahedron can be constructed. The first (left figures) can be obtained by combining six dodecahedra, each rotated by 1/10 ...

A rhombohedron is a parallelepiped bounded by six rhombi such that opposite faces are congruent. A rhombohedron having all six rhombic faces congruent is known as a trigonal ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...