We derive a local criterion for a plane near-triangulated graph to be perfect. It is shown that a plane near-triangulated graph is perfect if and only if it does not contain either a vertex, an edge or a triangle, the neighbourhood of which has an odd hole as its boundary. The characterization leads to an $O(n^2)$ algorithm for checking perfectness of plane near-triangulations.

中文翻译：

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完美的平面近三角剖分的局部特征

我们导出了一个平面近似三角图是完美的局部准则。结果表明，当且仅当平面近三角图不包含顶点，边或三角形时，它才是完美的，该顶点，边或三角形都不包含边界。表征导致$Ø（{ñ}^2）$ 平面近三角的完整性检查算法。