Weak-odd chromatic index of special digraph classes

Given a digraph D=(V(D),A(D)), let ∂D+(v)={vw|w∈ND+(v)} and ∂D−(v)={uv|u∈ND−(v)} be semi-cuts of v. A mapping φ:A(D)→[k] is called weak-odd k-edge coloring D if it satisfies the condition: for each v∈V(D), there at least one color with an odd number occurrences on non-empty semi-cut We call minimum integer k chromatic index D. When limit to 2 colors, def(D) denote defect D, i.e vertices in which above condition not satisfied. In this paper, we give descriptive characterization respect semicomplete digraphs extended tournaments, generalize results tournaments broader classes. addition, initiate study edge covering digraphs.