Explore the fascinating intersection of graph theory and knot theory in this 45-minute lecture. Delve into the concept of 4-colored graphs and their relationship to the complements of knots and links. Gain insights into how these mathematical structures can be used to analyze and understand the properties of knots and their surrounding spaces. Discover the connections between graph coloring and topological invariants, and learn how these techniques can be applied to classify and distinguish different types of knots and links.