Proper vertex coloring
= Proper vertex coloring
{title2=$\{u,v\}\in E\Longrightarrow c(u)\ne c(v)$}
= Proper vertex colouring
{synonym}
A proper vertex coloring assigns labels to the <vertices> of a <graph> so that <vertices> joined by an <edge> have different labels. Each <colour class> is an <independent set>. The <chromatic number> is the least number of labels needed for this form of <graph coloring>.