We introduce the fractional version of oriented coloring and initiate its study. We prove some basic results and study the parameter for directed cycles and sparse planar graphs. In particular, we show that for every $\epsilon > 0$, there exists an integer $g_{\epsilon} \geq 12$ such that any oriented planar graph having girth at least $g_{\epsilon}$ has fractional oriented chromatic number at most $4+\epsilon$. Whereas, it is known that there exists an oriented planar graph having girth at least $g_{\epsilon}$ with oriented chromatic number equal to $5$. We also study the fractional oriented chromatic number of directed cycles and provide its exact value. Interestingly, the result depends on the prime divisors of the length of the directed cycle.
翻译：我们引入了方向色素的分数版本, 并开始研究。 我们证明了一些基本结果, 并研究了定向周期和稀薄平面图的参数。 特别是, 我们显示, 对于每1美元 > 0美元, 我们存在一个整数 $g ⁇ epsilon}\geq 12 美元, 这样任何至少有 girth 至少 $ $ ⁇ epsilon} 的定向平面图的分数色谱数最多为 4 ⁇ silon$ 。 但是, 已知有一个方向的平面图, 其Girth $至少 $ $ ⁇ sipslon} $, 其方向色谱数等于 $ 5 美元。 我们还研究定向周期的分数, 并提供其准确值 。 有趣的是, 其结果取决于定向周期的粗差值 。
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