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arXiv · 2202.03178

A proof of the Kotzig-Ringel-Rosa Conjecture

Edinah K. Gnang
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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.

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Edinah K. Gnang. 2025-01-31. A proof of the Kotzig-Ringel-Rosa Conjecture. https://arxiv.org/abs/2202.03178

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