# Forced colorings with IGraph/M

Is it possible to force the colors of certain vertices in a graph so that the function which finds a minimum coloring will then extend the partial coloring with the fewest possible number of extra colors, without recoloring what has already been colored? If I understand the documentation of IGraph/M correctly, this is not quite possible, but maybe I am wrong. Am I correct in saying that the "ForcedColoring" option doesn’t quite allow this? Is there any other way to do this or otherwise hijack the IGMinimumVertexColoring function? This would be a great option if it were to be implemented, this is a frequent situation in coloring graphs, especially when you know something about the structure of your graph which allows you to quickly color part of it, having only a small part of the graph left to color with a minimum number of extra colors.

• I think the right place for IGraphM feature requests is here. – Jason B. Jun 25 at 18:28
• Thanks for the pointer. I would like to leave the question, in case someone knows a way to do this, in any way ... or if you suggest to delete, then maybe I will, please do say – EGME Jun 25 at 18:29
• @JasonB. Right, thanks as I said. Apparently, I don’t have access to that site (nor will creating an account work :( ... – EGME Jun 25 at 18:34
• @EGME you can definitely add a feature request. Make a GitHub account, login, go here: github.com/szhorvat/IGraphM/issues/new and write your request. The project is public and open on GitHub so anyone can leave a comment – b3m2a1 Jun 25 at 18:41
• @b3m2a1 Thanks, maybe I will try later, perhaps there is something wrong with my connection at the moment ... – EGME Jun 25 at 18:42

What you are asking for is not implemented in IGraph/M at the moment. You are correct that the "ForcedColoring" option doesn't quite do this at the moment. What it does is that it forces different colours on a set of vertices, but it is not currently possible to specify what those colours should be.