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Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

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 pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220).

A straight line embedding, or "straight line drawing," of a graph is a graph embedding in which all edges are drawn as straight line segments (as opposed to curves, etc.).

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).

Wagner's theorem states that a graph is planar iff it does not contain K_5 or K_(3,3) as a graph minor.

The Wormald graph is a unit-distance 4-chromatic graph with girth 5 on 13+5(13; 5)=6448 vertices.

The Loupekine snarks are the two snarks on 22 vertices and 33 edges illustrated above. They are implemented in the Wolfram Language as GraphData["LoupekineSnark1"] and ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...