On graceful labelings of trees

TL;DR

This paper proves the longstanding Graceful Labeling Conjecture for trees using a composition lemma, advancing understanding of graph labelings with implications for graph theory and combinatorics.

Contribution

It introduces a composition lemma that proves the Graceful Labeling Conjecture and its stronger form, resolving a major open problem in graph theory.

Findings

Proof of the Graceful Labeling Conjecture for trees

Introduction of a composition lemma for graph labelings

Establishment of a stronger version of the conjecture

Abstract

We prove via a composition lemma, the Kotzig-Ringel-Rosa conjecture, better known as the Graceful Labeling Conjecture. We also prove via a stronger version of the composition lemma a stronger form of the Graceful Labeling Conjecture.