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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
9
votes
What are some good examples of non-monotone graph properties?
Some natural non-monotone properties:
The property of being regular
The property of being a tree
The property of being Eulerian
9
votes
Accepted
Enumeration and random selection
Yes, there is formal way of saying this using complexity theory. I think the statement is something like: For all self-reducible relations, the problems of approximate sampling and approximate countin …
4
votes
Accepted
Finding a subgraph with slightly large size in planar graphs
I remember thinking about this a while ago, and stopped because it seemed unlikely that $log^2 n$ paths can be found in polynomial time. This was my argument, if I remember correctly.
The best know …