Proper orientations and proper chromatic number
The proper orientation number χ→(G) of a graph G is the minimum k such that there exists
an orientation of the edges of G with all vertex-outdegrees at most k and such that for any …
an orientation of the edges of G with all vertex-outdegrees at most k and such that for any …
Semi-proper orientations of dense graphs
An orientation D of a graph G is a digraph obtained from G by replacing each edge by
exactly one of the two possible arcs with the same ends. An orientation D of a graph G is a k …
exactly one of the two possible arcs with the same ends. An orientation D of a graph G is a k …
On the Proper Arc Labeling of Directed Graphs
An arc labeling ℓ ℓ of a directed graph G with positive integers is proper if for any two
adjacent vertices v, u, we have S_ ℓ (v) ≠ S_ ℓ (u) S ℓ (v)≠ S ℓ (u), where S_ ℓ (v) S ℓ (v) …
adjacent vertices v, u, we have S_ ℓ (v) ≠ S_ ℓ (u) S ℓ (v)≠ S ℓ (u), where S_ ℓ (v) S ℓ (v) …