What is vertex Colouring?

What is vertex Colouring?

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. The most common type of vertex coloring seeks to minimize the number of colors for a given graph.

What is graph coloring explain with example?

Graph coloring is the procedure of assignment of colors to each vertex of a graph G such that no adjacent vertices get same color. The objective is to minimize the number of colors while coloring a graph. The smallest number of colors required to color a graph G is called its chromatic number of that graph.

Is greedy coloring optimal?

The vertices of any graph may always be ordered in such a way that the greedy algorithm produces an optimal coloring. For, given any optimal coloring, one may order the vertices by their colors. Then when one uses a greedy algorithm with this order, the resulting coloring is automatically optimal.

Which is an example of a vertex coloring of a graph?

For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems are often stated and studied as is.

How does the edge coloring of a graph work?

In graph theory, edge coloring of a graph is an assignment of “colors” to the edges of the graph so that no two adjacent edges have the same color with an optimal number of colors. Two edges are said to be adjacent if they are connected to the same vertex.

What are the different types of edge coloring?

Edge colorings are one of several different types of graph coloring problems. The above figure of a Graph shows an edge coloring of a graph by the colors green and black, in which no adjacent edge have the same color. Use BFS traversal to start traversing the graph.

When do you use colors for vertex labels?

The terminology of using colors for vertex labels goes back to map coloring. Labels like red and blue are only used when the number of colors is small, and normally it is understood that the labels are drawn from the integers {1, 2, 3.}. A coloring using at most k colors is called a (proper) k-coloring.