The Graceful Tree Conjecture - Famous Math Problems

Explore the fascinating world of graph theory in this 34-minute video lecture on the Graceful Tree Conjecture. Delve into basic graph theory terminology, learn about graceful and non-graceful graphs, and examine evidence supporting the conjecture. Discover the Ringel-Kotzig conjecture's origins and its connection to vertex labellings introduced by A. Rosa in 1967. Engage with numerous exercises to investigate graceful labellings and gain insight into the important Coxeter Dynkin diagrams. Follow along as the lecture progresses through graph and tree terminology, graph labelling techniques, graceful labellings, and examples of graceful graphs before concluding with a discussion on the evidence supporting the Graceful Tree Conjecture.

Introduction
Graphs and trees terminology
Labelling of a graph
Graceful labellings
Graceful graphs
Evidence for the Graceful Tree Conjecture