A proof of the Kotzig-Ringel-Rosa Conjecture
Combinatorics
2025-02-03 v3
Abstract
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.
Cite
@article{arxiv.2202.03178,
title = {A proof of the Kotzig-Ringel-Rosa Conjecture},
author = {Edinah K. Gnang},
journal= {arXiv preprint arXiv:2202.03178},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2111.12812