Geodesic
Nonconvexity of the set of hypergraph degree sequences
Ricky Ini Liu1
1University of Michigan
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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It is well known that the set of possible degree sequences for a simple 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 simple $k$-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.
DOI : 10.37236/2719
Classification : 05C65, 05C07
Mots-clés : degree sequences, hypergraphs, zonotopes

Ricky Ini Liu  1

1 University of Michigan 
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Ricky Ini Liu. Nonconvexity of the set of hypergraph degree sequences. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2719

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