Colorings with neighborhood parity conditionPetruševski, Mirko (Avtor) Škrekovski, Riste (Avtor) planar graphsneighborhoodproper coloringodd coloringIn 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.20222023-01-30 09:52:27Članek v reviji144060UDK: 519.17ISSN pri članku: 0166-218XDOI: 10.1016/j.dam.2022.07.018COBISS_ID: 139308803sl