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In graph theory, a deletion-contraction formula / recursion is any formula of the following recursive form: = + (/). Here G is a graph, f is a function on graphs, e is any edge of G, G \ e denotes edge deletion, and G / e denotes contraction. Tutte refers to such a function as a W-function. [1]
A proper AVD-total-coloring of the complete graph K 4 with 5 colors, the minimum number possible. In graph theory, a total coloring is a coloring on the vertices and edges of a graph such that: (1). no adjacent vertices have the same color; (2). no adjacent edges have the same color; and (3). no edge and its endvertices are assigned the same color.
The concept was introduced by William K. Hale. [2] If T = {0} it reduces to common vertex coloring. The T-chromatic number, (), is the minimum number of colors that can be used in a T-coloring of G. The complementary coloring of T-coloring c, denoted ¯ is defined for each vertex v of G by
Therefore, the achromatic number of the Clebsch graph is 8. In graph theory, a complete coloring is a (proper) vertex coloring in which every pair of colors appears on at least one pair of adjacent vertices. Equivalently, a complete coloring is minimal in the sense that it cannot be transformed into a proper coloring with fewer colors by ...
A graph vertex coloring is a weak coloring, but not necessarily vice versa. Every graph has a weak 2-coloring. The figure on the right illustrates a simple algorithm for constructing a weak 2-coloring in an arbitrary graph. Part (a) shows the original graph. Part (b) shows a breadth-first search tree of the same graph. Part (c) shows how to ...
The graph coloring game is a mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring game, two players use a given set of colors to construct a coloring of a graph, following specific rules depending on the game we consider. One player tries to ...
The number e (e = 2.71828...), also known as Euler's number, which occurs widely in mathematical analysis; The number i, the imaginary unit such that = The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No two adjacent vertices have the same color, and The numbers of vertices in any two color classes differ by at most one.
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