The proper orientation number χ→(G) of a graph G is the minimum k such that there exists an edges with all vertex-outdegrees at most and for any adjacent vertices, outdegrees are different. Two major conjectures about resolved. First it shown, planar 14. Secondly, shown every graph, , where r=χ(G) usual chromatic maximum average degree taken over subgraphs G. Several other related results deriv...