c : V \rightarrow [k] where [k] := {1,2, \dots , k} such that c(u) \neq c(v) if uv \in E and c(u) < c(v) if \overrightarrow{uv} \in A [REF].
c : V \rightarrow [k] where [k] := {1,2, \dots , k} such that c(u) \neq c(v) if uv \in E and c(u) \leq c(v) if \overrightarrow{uv} \in A [REF].