Graph Coloring Applications: Scheduling, Frequencies & Registers | Discrete Mathematics §10.8

The reason your phone can reuse the same frequency as a tower two cities away — and the reason a compiler can pack your variables into a handful of registers — is the same idea: graph coloring in disguise. In this video: three classic applications, worked on the board. Exam scheduling — build a conflict graph where an edge means two courses share a student, color it, and each color is a time slot (a clique of four courses forces at least four slots). Frequency assignment — vertices are stations, edges join stations close enough to interfere, colors are channels, and far-apart stations safely reuse a color, which is exactly the cellular principle. Register allocation — vertices are variables, edges join variables live at the same time, colors are registers, and if the chromatic number exceeds the registers available, something must spill. One coloring engine behind all three. This video is part of Discrete Mathematics · Graphs (§10.8 — Graph Coloring). Full section playlist linked above / in the description on the channel. Made with the Engineering Simplified method: a calm, two-voice story lesson taught on a chalk-and-board, with every definition and example drawn out step by step. Topic coverage follows Rosen, Discrete Mathematics and Its Applications (Chapter 10).