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So I'm asked to find the chromatic number for the given graph by colouring the vertices using the minimum number of required colours. My attempt at doing so is below but I was wondering if someone could confirm whether I coloured it correctly? Are there any vertices that should be a different colour/should there be more or less colours used? Did I misplace any colours?

I was also wondering if there is some rule or formula to figure out the chromatic number for a graph?

I'd appreciate some help or confirmation.

Link to graph: https://imgur.com/a/1UVydLo

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    $\begingroup$ You shouldn't include a link to an image. Rather the image directly itself. You link point to a website, using cookies and collecting data, that we may not want to go to. Furtermore, a direct image is safer for future reference $\endgroup$ – Thomas Lesgourgues Jun 10 at 7:45
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Nodes $8, 14, 15$ form a triangle. Therefore it is not possible to color the graph with less than $3$ colors. Since you used $3$ colors and no two adjacent nodes have the same color, your coloring is correct.

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