Recursive Colorings of Graphs

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Abstract
A graph G is an ordered pair G = (V, E) where E is a set of 2-element subsets of V. The set V is the set of vertices, and E is the set of edges. The vertices x and y are joined by an edge if {x, y} is an edge. If X is a set (of colors) and χ : V →X, then we say that χ is an X-coloring of G if whenever two vertices x and y are joined by an edge, then χ(x) ≠ x(y). A graph is X-colorable if there is an χ-coloring of it. We will identify the natural number n with the set {0, 1, …, n – 1}, and often refer to n-colorings and to graphs being n-colorable.

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