A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$‐extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5‐connected triangulation on the projective plane of even order is distance 3 7‐extendable and distance 4 $m$‐extendable for any $m$.

中文翻译：

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投影平面图中的边缘接近度和匹配扩展

图 $G$ 至少 $2米+2$ 顶点被称为距离 $d$ $米$对于任何匹配，可扩展 $\mathrm{中号}$ 的 $G$ 与 $米$ 边缘至少相距一定距离的边缘 $d$ 成对存在 $G$ 包含 $\mathrm{中号}$。在本文中，我们证明了偶数投影平面上的每5个连接三角剖分距离为3 7可扩展且距离为4$米$可扩展为任何 $米$。