On graceful labelings of trees
Edinah K. Gnang

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.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems
