In this work we consider arc criticality in colourings of oriented graphs. We study deeply critical oriented graphs, those graphs for which the removal of any arc results in a decrease of the oriented chromatic number by $2$. We prove the existence of deeply critical oriented cliques of every odd order $n\geq 9$, closing an open question posed by Borodin et al. (Journal of Combinatorial Theory, Series B, 81(1):150-155, 2001). Additionally, we prove the non-existence of deeply critical oriented cliques among the family of circulant oriented cliques of even order.

中文翻译：

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论极度批判的集团

在这项工作中，我们考虑了定向图着色中的电弧临界度。我们研究了深度临界定向图，这些图的任何弧形去除都会导致定向色数减少$ 2 $。我们证明了每个奇数阶$ n \ geq 9 $都存在着以深层批判为导向的集团，从而解决了Borodin等人提出的一个开放性问题。（Journal of Combinatorial Theory，Series B，81（1）：150-155，2001）。此外，我们证明了在偶数阶的循环定向派系家族中不存在深度批判导向派系。