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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.

2 votes

Acyclicity equivalent to unique paths

I think the most straightforward generalization would be to algebraic topology. The analogue to acyclicity is the property of being simply connected, and uniqueness of a path between two vertices beco …
Kevin Ventullo's user avatar
14 votes
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Does a graph with all vertex degrees divisible by 3 contain a cubic subgraph?

Counterexample: alt text http://www.freeimagehosting.net/newuploads/8m77r.png
Kevin Ventullo's user avatar