Graph Colouring
Lesson notes
Overview
Give adjacent nodes different colours using as few as possible: scheduling and map colouring. This topic is rated beginner and is number 77 of 117 in Computer Science. Core ideas and first intuitions. No prior knowledge needed.
What you are seeing
The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
Graph colouring assigns colours to nodes so that no two adjacent nodes share a colour, using as few colours as possible. It models scheduling exams without clashes, assigning radio frequencies and allocating registers in compilers. The minimum number is the chromatic number, and finding it is NP-hard, so greedy heuristics are common. The four colour theorem says that any map can be coloured with four colours.
Reading the relationship
The expression "greedy colouring" is a compact summary of the idea. It uses the symbols g, r, e, d, y, c; name what each one stands for before you start. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.
Try this
Start by only moving one slider at a time. Say aloud what you expect, then check.
Common pitfalls
Test small inputs by hand and then the largest ones. Off-by-one errors and forgetting how cost grows with input size are the most common traps.
How it connects
It builds on “Minimum Spanning Tree on a Larger Graph”, the topic before it in Computer Science. Once you are comfortable, continue with “PageRank on a Larger Web”.
Why it matters
Computing ideas decide how fast, how safely and how well software can solve problems.
Where you might use it
- Revising “Graph Colouring” before a class, exam or certification
- Choosing the right algorithm or data structure when writing software or apps
- Debugging programs and judging how fast or how safely code will run at scale
- Understanding how search engines, games, phones and AI systems make decisions
Frequently asked questions
What is Graph Colouring?
Give adjacent nodes different colours using as few as possible: scheduling and map colouring. It is a beginner topic in Computer Science.
How do I use the Graph Colouring simulation?
The panel at the top shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression greedy colouring packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Minimum Spanning Tree on a Larger Graph”, the previous topic in Computer Science. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.