Lesson 180
Graph Coloring
Chromatic Number & Greedy
1:00How to assign colors to graph vertices so no two neighbors match — and why this simple rule underlies scheduling, compilers, and NP-hardness.
By the end, you can
- State the proper coloring rule and explain what each edge constraint means.
- Define the chromatic number and compute it for small standard graphs (paths, cycles, complete graphs, stars).
- Trace the greedy coloring algorithm on a small graph and identify the Δ+1 bound.
- Explain why greedy is order-sensitive and how Welsh-Powell chooses vertex order.
- Apply Brooks' theorem and state its two exceptions.
- Determine whether a graph is 2-colorable by checking for odd cycles.
- Map scheduling, register allocation, and frequency assignment onto the graph coloring framework.
- State the Four Color Theorem and its historical significance.
- Distinguish the easy case (2-colorability) from the NP-complete cases (k ≥ 3).
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