Types Of Coloring In Graph Theory, Exact Coloring Wikipedia
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A k edge coloring of g is an assignment of k colors to the edges of g in such a way that any two edges meeting at a common vertex are assigned different colors.
Hello kitty cartoon coloring pages. In the above graph there is only one vertex v without any edge. In a graph no two adjacent vertices adjacent edges or adjacent regions are colored with minimum number of colors. A simple graph which has n vertices the degree of every vertex is at most n 1.
This number is called the chromatic number and the graph is called a properly colored graph. A trivial graph is the graph which has only one vertex. Therefore it is a trivial graph.
We will discuss only a certain few important types of graphs in this chapter. A simple graph is the undirected graph with no parallel edges and no loops. One may also consider coloring edges possibly so that no two coincident edges are the same color or other variations.
Let g be a graph with no loops. If g is the complete graph k n then p g k kk 1k 2. The smallest number of colors needed for an edge coloring of a graph g is the chromatic index or edge chromatic number x g.
Many problems and theorems in graph theory have to do with various ways of coloring graphs. There are various types of graphs depending upon the number of vertices number of edges interconnectivity and their overall structure. In the above graph there are three vertices named a b and c.
Typically one is interested in coloring a graph so that no two adjacent vertices have the same color or with other similar restrictions. A tait coloring is a 3 edge coloring of a cubic graph. The four color theorem is equivalent to the assertion that every planar cubic bridgeless graph admits a tait coloring.
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