Adjacent strong edge coloring of graphs (Q1609524)

A proper edge coloring of a graph is an adjacent strong edge coloring if, for every adjacent vertices \(u\) and \(v\), the set of colors of all edges at \(u\) is different from the set of all colors of edges at \(v\). The authors determine the minimum number \(k\) such that a tree (a cycle, a complete graph) has an adjacent strong edge coloring with \(k\) colors. They then conjecture that every connected graph with at least six vertices has an adjacent strong edge coloring with at most maximum degree plus two colors. The paper is poorly written.