6 papers · 1 filter
A Helly-Type Theorem for two-component convex sets
Giuliamaria Menara
In any fixed dimension, consider a finite collection of sets, each consisting of exactly two disjoint, closed, convex pieces. We show that to guarantee the intersection of the whol…
Coloring semiminimal Cayley Graphs
Ignacio García-Marco, Kolja Knauer, Giuliamaria Menara
In 1978 Babai raised the question whether all semiminimal Cayley graphs have bounded chromatic number. In this paper we show that semiminimal Cayley graphs of abelian and generaliz…
Combinatorial Designs and Cellular Automata: A Survey
Luca Manzoni, Luca Mariot, Giuliamaria Menara
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebra…
Eulerian magnitude homology: diagonality, injective words, and regular path homology
Luigi Caputi, Giuliamaria Menara
In this paper we explore the algebraic structure and combinatorial properties of eulerian magnitude homology. First, we analyze the diagonality conditions of eulerian magnitude hom…
On torsion in eulerian magnitude homology of Erdos-Renyi random graphs
Giuliamaria Menara
In this paper we investigate the regimes where an Erdos-Renyi random graph has torsion free eulerian magnitude homology groups. To this end, we start be introducing the eulerian As…
Eulerian magnitude homology: subgraph structure and random graphs
Chad Giusti, Giuliamaria Menara
In this paper we explore the connection between the ranks of the magnitude homology groups of a graph and the structure of its subgraphs. To this end, we introduce variants of magn…