Perfect Graphs

This is a final project for MATH 1230: Graph Theory.

References:
[1] Maria Chudnovsky*, Gérard Cornuéjols**, Xiao Liu†, Paul Seymour, and Kristina Vušković,
Recognizing berge graphs, Combinatorica 25 (2005), no. 2, 143–186.
[2] Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas, The strong perfect graph
theorem, Annals of Mathematics 164 (2006), no. 1, 51–229.
[3] László Lovász, Normal hypergraphs and the perfect graph conjecture, Discrete Mathematics 2
(1972), no. 3, 253–267.

[alexduchnowski]

Erratum:
At 5:37, we claim that only the top graphs have holes of length 5. In fact, the graph with a hole of length 9 also has a hole of length 5, in fact it has several, as well as a hole of length 7, though we use the hole of length 9 to show the generalization to larger holes.

[elijahberegovsky]

Hey! A new maths channel! Cool video, guys! Are you going to specialize on graph theory (my beloved) or maths in general?

[markraya]

What a great video. I really hope you guys plan on doing more of these

[elytrae]

can you givea programming video on how to make math visuals?

[korigamik]

This is great! Can you share the source code for this video?

[Luiz-rteo]

But will the procedure you described at the end of the video generate all perfect graphs of order n? If i, for example, create an algorithm that adds all choices in a queue (add a isolated vertex or a dominating vertex) and executes them until I have added n vertices the queue is empty, will that generate all possible perfect graphs or size n?