Remarks on odd colorings of graphs

A proper vertex coloring ? of graph G is said to be odd if for each non-isolated x?V(G) there exists a color c such that ??1(c)?N(x) odd-sized. The minimum number colors in any G, denoted ?o(G), the chromatic number. Odd colorings were recently introduced Petruševski and Škrekovski (0000). Here we discuss various basic properties this new parameter, characterize acyclic graphs hypercubes terms number, establish several upper bounds regard degenericity or maximum degree, pose questions problems.