Explore cutting-edge graph theory concepts in this 24-minute IEEE conference talk covering light spanners, low-treewidth embeddings, and efficient traversing in minor-free graphs. Delve into Capacitated Vehicle Routing, Subset TSP, and techniques for designing Polynomial-Time Approximation Schemes (PTAS). Learn about light preservers, local spanners, and their applications in planar graphs with vortices. Examine tree structures of clique-sums in nearly-embedded graphs and discover open problems in the field. Gain insights from researchers Vincent Cohen-Addad, Arnold Filtser, Philip N. Klein, and Hung Le as they present advanced algorithms and graph theory applications.