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147  Articles
1 of 16 pages  |  10  records  |  more records»
The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated. The signless normalized Laplacian is introduced and it is shown that its spectrum for classical hypergraphs coincides with the spectrum of the normalized Lap... see more

The search for the smallest possible dd-regular graph of girth gg has a long history, and is usually known as the cage problem. This problem has a natural extension to hypergraphs, where we may ask for the smallest number of vertices in a dd-regular, rr-u... see more

We consider a robust variant of Dirac-type problems in kk-uniform hypergraphs. For instance, we prove that if H\mathcal{H} is a kk-uniform hypergraph with minimum codegree at least (12+?)n\left(\frac 12 + \gamma \right)n, ?>0\gamma >0, and nn is suffic... see more

In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set of disjoint edges one edge at a time; then we analyze the independent proc... see more

We develop a connection between DP-colorings of kk-uniform hypergraphs of order nn and coverings of nn-dimensional Boolean hypercube by pairs of antipodal (n-k)(n-k)-dimensional faces. Bernshteyn and Kostochka established a lower bound on the number of ed... see more

In this paper, we study the spectra of regular hypergraphs following the definitions from Feng and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the random regular hypergraphs. We then relate the second eigenvalues t... see more

Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an rr-factorization of a complete 33-uniform hypergraph on mm vertices, K3mK_m^3, to an ss... see more

In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set of disjoint edges one edge at a time; then we analyze the independent proc... see more

In 2007 Matamala proved that if G is a simple graph with maximum degree ? = 3 not containing K?+1 as a subgraph and s, t are positive integers such that s+t = ?, then the vertex set of G admits a partition (S,T) such that G[S] is a maximum order (s-1... see more

1 of 16 pages  |  10  records  |  more records»