着色多边形可见图及其推广
Colouring polygon visibility graphs and their generalizations
摘要：
曲线伪可见图推广了多边形和伪多边形可见图，形成了一类遗传图。证明了团数为$ω$的曲线伪可见图的色数至多为$3\cdot 4^{ω-1}$。证明是通过设置有序图，我们确定了两个条件满足的每一个曲线伪可见图（被认为是一个有序图），并证明他们是足够的要求的界限。证明是算法的：团数和具有所声称的颜色数的着色都可以在多项式时间内计算。
英文摘要：
Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number $ω$ has chromatic number at most $3\cdot 4^{ω-1}$. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.
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