8 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…
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 inequ…
Uniform density in matroids, matrices and graphs
Karel Devriendt, Raffaella Mulas
We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a…
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…
Maximal colourings for graphs
Raffaella Mulas
We consider two different notions of graph colouring, namely, the -periodic colouring for vertices that has been introduced in 1974 by Bondy and Simonovits, and the periodic col…