Label the graph’s vertices with colors such that no two vertices sharing the same edge have the same color.[br]The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted ch. Determine the chromatic number of each connected graph.[br]If the number of conflicts is shown, that means there aren't enough colors.[br]If the number of lapse is shown that means there are redundancies (non adjacent colors need to be changed).

[url=https://en.wikipedia.org/wiki/Graph_coloring]Graph coloring[/url] enjoys many practical applications as well as theoretical[br] challenges. Beside the classical types of problems, different [br]limitations can also be set on the graph, or on the way a color is [br]assigned, or even on the color itself. It has even reached popularity [br]with the general public in the form of the popular number puzzle [url=https://en.wikipedia.org/wiki/Sudoku]Sudoku[/url]. Graph coloring is still a very active field of research.