Some remarks on odd edge colorings of digraphsPetruševski, Mirko (Avtor) Škrekovski, Riste (Avtor) digraphodd edge coloringodd chromatic indexThe principal aim of this article is to initiate a study of the following coloring notion for digraphs. An odd k-edge coloring of a general digraph (directed pseudograph) D is a (not necessarily proper) coloring of its edges with at most k colors such that for every vertex v and color c holds: if c is used on the set ∂$_D$(v) of edges incident with v, then c appears an odd number of times on each non-empty set from the pair ∂$^+_D$(v), ∂$^−_D$(v) of, respectively, outgoing and incoming edges incident with v. We show that it can be decided in polynomial time whether D admits an odd 2-edge coloring. Throughout the paper, several conjectures, questions and open problems are posed. In particular, we conjecture that for each odd edge-colorable digraph four colors suffice.20212022-02-10 08:41:11Članek v reviji134879UDK: 519.17ISSN pri članku: 2227-7390DOI: 10.3390/math9030231COBISS_ID: 49625347sl