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Its easy to show that the chromatic number of a planar graph is no more than six.

Graph coloring minimum number of colors. De nition 16 Chromatic Number. Brooks Theorem A connected simple graphs chromatic number is no larger than the maximum. That is if uv E then F u6 F v.

The graph is planar and definitely requires four colours. The code should also return false if the graph. The given graph may be properly colored using 3 colors as shown below- Problem-05.

It is not doable with 2 colors since we have subgraph K 3. Graph coloring can be used to find the minimum number of time slots needed to create a schedule with no time conflicts. An array colorV that should have numbers from 1 to m.

The following is now a very natural concept. A value graphij is 1 if there is a direct edge from i to j otherwise graphij is 0. So four colors are needed to properly color the graph.

Colori should represent the color assigned to the ith vertex. This problem was first posed in the nineteenth century and it was quickly conjectured that in all cases four colors suffice. The chromatic number of a graph is the minimum number of colors in a proper coloring of that graph.

The graphs that can be 1-colored are called edgeless graphs. The task is to find the minimum number of colors needed to color the given graph. Hence the count is 3.

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