论文标题
关于图形奇数的备注
Remarks on odd colorings of graphs
论文作者
论文摘要
如果每个非分离顶点$ x \ in V（g）$中存在一个颜色$ c $，则适当的顶点着色$ g $是奇怪的。 $ g $的任何奇数颜色（表示为$χ_o（g）$）的最小颜色是奇数的色度数字。最近在[M.〜petruševski，R .〜škrekovski：\ textit {带有邻居奇偶校验条件的颜色}]中引入了奇数。在这里，我们讨论了该新图表参数的各种基本属性，以奇数色数来表征无环图和超振管，建立了关于退化性或最高程度的几个上限，并提出了几个问题和问题。
A proper vertex coloring $φ$ of graph $G$ is said to be odd if for each non-isolated vertex $x\in V(G)$ there exists a color $c$ such that $φ^{-1}(c)\cap N(x)$ is odd-sized. The minimum number of colors in any odd coloring of $G$, denoted $χ_o(G)$, is the odd chromatic number. Odd colorings were recently introduced in [M.~Petruševski, R.~Škrekovski: \textit{Colorings with neighborhood parity condition}]. Here we discuss various basic properties of this new graph parameter, characterize acyclic graphs and hypercubes in terms of odd chromatic number, establish several upper bounds in regard to degenericity or maximum degree, and pose several questions and problems.
