Even order uniform hypergraph via the Einstein product

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

The Laplacian of a uniform hypergraph

In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0, 2], and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H+-eigenvalues of the Laplacian and all the smallest H+-eigenvalues of its sub-t...

The Hardness of 3 - Uniform Hypergraph Coloring

We prove that coloring a 3-uniform 2-colorable hypergraph with c colors is NP-hard for any constant c. The best known algorithm [20] colors such a graph using O(n1/5) colors. Our result immediately implies that for any constants k ≥ 3 and c2 > c1 > 1, coloring a k-uniform c1-colorable hypergraph with c2 colors is NP-hard; the case k = 2, however, remains wide open. This is the first hardness re...

Identifying High Order Brain Connectome Biomarkers via Learning on Hypergraph

A census of one-factorizations of the complete 3-uniform hypergraph of order 9

The one-factorizations of the complete 3-uniform hypergraph with 9 vertices, K 9 , are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such one-factorizations is 103 000.