Discrete Math › Section C · Graph theory › Topic C.12
Partial orders
Some things can be ranked and some cannot. A course can require another, a file can depend on another, one set can sit inside another, yet many pairs are simply unrelated. Partial orders describe this kind of ranking precisely, and topological sorting turns one into a workable schedule.
In this topic
- Rankings with gaps
- The definition
- Comparable and incomparable
- Hasse diagrams
- Worked example: divisors of 12
- Maximal, greatest, minimal, least
- Worked example: several maximal elements
- Topological sorting
- Worked example: scheduling courses
- Lattices
- Common mistakes to avoid
- Key takeaways
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