Editing Uniquely colorable graph (section)

{{short description|Graph with only one possible coloring}}

In [[graph theory]], a '''uniquely colorable graph''' is a {{mvar|k}}-chromatic [[Graph (discrete mathematics)|graph]] that has only one possible (proper) {{mvar|k}}-[[Graph coloring|coloring]] up to [[permutation]] of the colors.  Equivalently, there is only one way to [[Graph partition|partition]] its [[Vertex (graph theory)|vertices]] into {{mvar|k}} [[independent set (graph theory)|independent set]]s and there is no way to partition them into {{math|''k'' − 1}} independent sets.