论文标题
关于圆形弧形的力量
On powers of circular arc graphs
论文作者
论文摘要
一类图形$ \ MATHCAL {C} $在\ Mathcal {C} $中的每个图$ g \以及\ Mathbb {n} $，$ g^k \ in \ Mathcal {c} $中关闭。如果在\ at \ mathbb {n} $中的每一个$ k \ in \ g^k \ in \ Mathcal {c} $中，则$ \ MATHCAL {C} $在powers下是强烈关闭的，则是$ g^k \ in \ mathcal {c} $，则是$ g^{k+1} \ in \ mathcal in \ mathcal {c} $。众所周知，圆形弧形图和适当的圆弧图在功率下封闭。但是，这些类别的图表是否在力量下也很牢固，这是开放的。在本文中，我们解决了这些问题。
A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular arc graphs and proper circular arc graphs are closed under powers. But it is open whether these classes of graphs are also strongly closed under powers. In this paper we have settled these problems.
