In relation to oriented coloring and chromatic number, the parameter oriented relative clique number of an oriented graph $\overrightarrow{G}$, denoted by $\omega_{ro}(\overrightarrow{G})$, is the main focus of this work. We solve an open problem mentioned in the recent survey on oriented coloring by Sopena (Discrete Mathematics 2016), and positively settle a conjecture due to Sen (PhD thesis 2014), by proving that the maximum value of $\omega_{ro}(\overrightarrow{G})$ is $10$ when $\overrightarrow{G}$ is a planar graph.

翻译：关于方向颜色和染色编号,以 $\ omega ⁇ ro} (\ overrightrorror{G}) 表示的面向方向图形 $\ overrightrow{G} $ 的参数相对组号是这项工作的主要焦点。 我们解决了最近Sopena 方向颜色调查(2016年 Discrete Maistics) 中提到的一个未解决的问题,并通过证明$\ omega ⁇ ro} (\ overrightrowr{G}) 的最大值为$ 100 美元, 而 $\ overrightrowr{G} $ 是一张平面图, 并积极解决了因 Sen 引起的猜想( PhD Thesis 2014 ), 证明 $\\ omega} (\ overrightrow{G} $ 最高值为 $ 100 美元 。