3 research outputs found
Independence numbers of hypergraphs with sparse neighborhoods
AbstractLet H be a hypergraph with N vertices and average degree d. Suppose that the neighborhoods of H are sparse, then its independence number is at least cN(logd /d), where c>0 is a constant. In particular, let integers r≥3 and n≥1 be fixed, and let H be r-uniform, triangle-free and linear, then its independence number is at least cNlognd/d for all sufficiently large d
Coloring the normalized Laplacian for oriented hypergraphs
The independence number, coloring number and related parameters are
investigated in the setting of oriented hypergraphs using the spectrum of the
normalized Laplace operator. For the independence number, both an inertia--like
bound and a ratio--like bound are shown. A Sandwich Theorem involving the
clique number, the vector chromatic number and the coloring number is proved,
as well as a lower bound for the vector chromatic number in terms of the
smallest and the largest eigenvalue of the normalized Laplacian. In addition,
spectral partition numbers are studied in relation to the coloring number.Comment: Linear Algebra and Its Applications, To appea