6 papers · 1 filter
Cheeger-type inequalities for the second largest spectral gap from of the normalized Laplacian
Lies Beers, Raffaella Mulas, Jan Petr
We study the second largest spectral gap from of the normalized Laplacian of a graph, a quantity that appears in the literature in connection with random walks, expander graphs…
Spectral Perspectives on FAT Graph Colorings
Lies Beers, Raffaella Mulas
We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while t…
Fair and Tolerant (FAT) Graph Colorings
Lies Beers, Raffaella Mulas
We introduce and study Fair and Tolerant colorings (FAT colorings), where each vertex tolerates a given fraction of same-colored neighbors while fairness is preserved across the ot…
Coloring outside the lines: Spectral bounds for generalized hypergraph colorings
Lies Beers, Raffaella Mulas
It is known that, for an oriented hypergraph with (vertex) coloring number and smallest and largest normalized Laplacian eigenvalues and , respectively, the inequali…
Extremal Betti Numbers and Persistence in Flag Complexes
Lies Beers, Magnus Bakke Botnan
We investigate several problems concerning extremal Betti numbers and persistence in filtrations of flag complexes. For graphs on vertices, we show that is maximal…
At the end of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian
Lies Beers, Raffaella Mulas
For a graph with largest normalized Laplacian eigenvalue and (vertex) coloring number , it is known that . Here we prove properties of graphs for which th…