Please use words to describe the solution process.
Let G be a properly colored graph and let us suppose that one of the colours used is red. The set of all red-coloured vertices have a special property. What is it?
Graph colouring can be thought of as partitioning V(G) into subsets with this special property.
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A coloring problem is solved. The solution received a rating of "5" from the student who posted the question.