20.500.12556/RUL-134879 Some remarks on odd edge colorings of digraphs The 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. digraph odd edge coloring odd chromatic index digraf liho povezavno barvanje lihi kromatični indeks true false true Angleški jezik Slovenski jezik Članek v reviji 2022-02-10 08:41:11 2022-02-10 08:41:12 2022-09-14 04:10:27 0000-00-00 00:00:00 2021 0 0 10 str. iss. 3, art. 231 Vol. 9 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2227-7390 10.3390/math9030231 49625347 RAZ_Petrusevski_Mirko_2021.pdf RAZ_Petrusevski_Mirko_2021.pdf 1 A4BA241B62BF90168C1218447CF440BD 039fb3b819f46d2a97e456a4ecf59f7659db4a33172ed239e9c84ccda45c6df1 dd63470e-8a44-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153596 https://www.mdpi.com/2227-7390/9/3/231 0 b3322b2c-8a44-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153595 Fakulteta za matematiko in fiziko 0 0 0