Upper Bounds of the Odd Chromatic Number of a Graph in terms of its Thickness

An odd coloring of a graph G is a proper vertex coloring with the property that for each non-isolated vertex v V (G), there exists a color c such that the cardinality of ^-1 (c) N (v) is odd. The concept of odd colorings is introduced by Petrusevski and Skrekovski. In this paper, we investigate upper bounds of the odd chromatic number of a graph in terms of its thickness and other graphical parameters. In particular, we show that a graph G with the minimum degree at least 2 (G) -1 and girth at least 6 is odd 6 (G) -colorable, where (G) is the thickness of G.