Kotzig-Ringel-Rosa猜想的证明
A proof of the Kotzig-Ringel-Rosa Conjecture
AI总结：
本文通过泛函重构和组合引理，证明了图论中长期存在的Kotzig-Ringel-Rosa猜想，即每棵树都存在优美标号。
摘要：
在图论中，具有m条边的图的优美标号是用0到m（含）之间的整数子集对其顶点进行标号，使得没有两个顶点共享同一标号，且每条边由其端点标号绝对差唯一标识。Kotzig-Ringel-Rosa猜想断言每棵树都存在优美标号。我们通过该猜想的泛函重构和一个组合引理证明了这一长期存在的猜想。
英文摘要：
In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with a subset of the integers ranging from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference of labels assigned to its endpoints. The Kotzig-Ringel-Rosa conjecture asserts that every tree admits a graceful labeling. We provide a proof of this long standing conjecture via a functional reformulation of the conjecture and a composition lemma.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
