20.500.12556/RUL-144060 Colorings with neighborhood parity condition In this short paper, we introduce a new vertex coloring whose motivation comes from our series on odd edge-colorings of graphs. A proper vertex coloring $\varphi$ of a graph $G$ is said to be odd if for each non-isolated vertex $x \in V(G)$ there exists a color $c$ such that $\varphi^{-1}(c) \cap N(x)$ is odd-sized. We prove that every simple planar graph admits an odd 9-coloring, and conjecture that 5 colors always suffice. planar graphs neighborhood proper coloring odd coloring ravninski grafi soseščina dobro barvanje liho barvanje true false true Angleški jezik Slovenski jezik Članek v reviji 2023-01-30 09:52:27 2023-01-30 09:52:28 2023-01-31 03:47:53 0000-00-00 00:00:00 2022 0 0 Str. 385-391 Vol. 321 Nov. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 0166-218X 10.1016/j.dam.2022.07.018 139308803 1-s2.0-S0166218X22002803-main.pdf 1-s2.0-S0166218X22002803-main.pdf 1 1A931325A3495F66918020D76A1C082F cd78d70269e29f4bac4f6bfa7d07ecf0689013b13504cf17ced524821314d336 ad03f5bf-a07b-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166185 https://www.sciencedirect.com/science/article/pii/S0166218X22002803 1 279999ac-a07b-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166184 Fakulteta za matematiko in fiziko 0 0 0