The KRR via a Composition Lemma Part 1

Abstract. In graph theory, a graceful labeling of a graph with m edges is a labeling of its vertices with some subset of the integers from 0 to m inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints. The Kotzig-Ringel-Rosa conjecture asserts that every tree admits a graceful labeling. We provide a short proof of this long standing conjecture via a functional reformulation of the conjecture and a composition lemma.