Nonconvexity of the set of hypergraph degree sequences

Details Nonconvexity of the set of hypergraph degree sequences Nonconvexity of the set of hypergraph degree sequences

2012-01-28

arxiv.org/abs/1201.5989v1

Mathematics

Combinatorics

5 pages

Scientific paper

It is well known that the set of possible degree sequences for a graph on $n$ vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a $k$-uniform hypergraph on $n$ vertices is not the intersection of a lattice and a convex polytope for $k \geq 3$ and $n \geq k+13$. We also show an analogous nonconvexity result for the set of degree sequences of $k$-partite $k$-uniform hypergraphs and the generalized notion of $\lambda$-balanced $k$-uniform hypergraphs.

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