AI 中文总结
本文确定极大平面图的类边重构数界为1或2，通过分析可翻转边删除后的补全方式等论证，解决了2010年重构数综述提出的问题。
AI 中文摘要
图的边卡片是删除一条边后得到的图，类边重构数指当已知图所属类别时，用于唯一确定该图所需的最少精心选取的边卡片数量。本文确定了极大平面图的类边重构数的严格通用界：选取2张边卡片总是足够的，而八面体图表明2张是必要的；部分极大平面图仅需1张边卡片即可被唯一确定。论证利用了可翻转边被删除后会留下一个四边形，其两条对角线构成仅有的极大平面补全方式，度数信息可排除竞争补全，对含3度顶点的图另有单独论证。这解决了2010年一篇关于重构数综述中提出的问题。
英文摘要
An edge card of a graph is obtained by deleting one edge, and a class edge-reconstruction number asks for the fewest carefully selected cards that identify the graph when its class is known. We determine the sharp universal bound for maximal planar graphs. Two selected cards always suffice, and the octahedral graph shows that two can be necessary; some maximal planar graphs are already identified by one card. The argument exploits the fact that deleting a flippable edge leaves a single quadrilateral whose two diagonals give the only possible maximal-planar completions. Degree information then rules out the competing completion, with a separate argument for graphs containing a vertex of degree three. This settles a problem posed in a 2010 survey on reconstruction numbers.
