You may want to download the lecture slides that were used for these videos (PDF).
1. Interval Orders
This video reviews interval orders and describes an example. (1:51)
2. Characterizing Interval Orders
Some posets are interval orders, some are not. Fishburn’s Theorem (1970) gives us a necessary and sufficient condition for determining whether a poset is an interval order. This video provides the proof that an interval order cannot contain a 2 + 2. (7:32)
3. Characterizing Interval Orders, Continued
This video completes our proof by proving sufficiency. (13:55)
4. Interval Order Algorithm
Now that we have a proof of Fishburn’s Theorem, we need an easily implementable algorithm. This video discusses how to find whether a 2 + 2 exists in a poset algorithmically. (6:57)
5. Interval Order Algorithm, Continued
This video discusses how to write a poset as an interval order when a 2 + 2 is not present. (19:07)
6. Interval Order Algorithm (Summary)
This brief video summarizes how the interval order algorithm works. (1:17)
7. More on the Interval Algorithm
This video describes more on the output of the algorithm, and how there are additional exercises in the textbook where you can try to implement the algorithm. (2:30)
8. Recognizing Interval Graphs
If we are given a graph, can we determine whether it is an interval graph? How can we tell? This video gives an implementable and efficient algorithm for answering this question. (4:49)
9. Example of Determining Whether a Graph is an Interval Graph
This video gives an example of the polynomial time algorithm we introduced for determining whether a graph is an interval graph. (15:30)
10. Forbidden Subgraphs for Interval Graphs
This video summarizes the main ideas of this lecture, discusses some of the history behind testing whether a graph is an interval graphs, and lists a number of constructive things that you should be able to do with the theorems and algorithms we introduced in this lecture. (3:03)