论文标题
面向的相对集团无三角形平面图为10
The oriented relative clique number of triangle-free planar graphs is 10
论文作者
论文摘要
与定向的着色和色数有关，以参数为导向的相对集团$ \ overrightArrow {g} $的相对集团，由$ω__{ro}表示（\ oferrightArrow {g}）$，是这项工作的主要重点。我们解决了Sopena（离散数学2016）对定向着色的最新调查中提到的一个空旷的问题，并通过证明$ 10 $ 10 $ $ 10 $ $ \ contrawrow IS A Plancar at Clancar a clagraur图，从而证明了$ω__{RO} $ 10 $ a的最大价值，从而确定了由于Sen（Phd论文2014）的猜想（Phd论文2014）。
In relation to oriented coloring and chromatic number, the parameter oriented relative clique number of an oriented graph $\overrightarrow{G}$, denoted by $ω_{ro}(\overrightarrow{G})$, 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 $ω_{ro}(\overrightarrow{G})$ is $10$ when $\overrightarrow{G}$ is a planar graph.
