We introduce the notion of star cluster of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen ...

Let G(n,α) be the class of block graphs on n vertices and prescribed independence number α. In this article we prove that the maximum spectral radius ρ(G), among all graphs G∈G(n,α), is reached at a unique graph. As a ...

The analogue of Hadwiger's conjecture for the immersion order states that every graph G contains Kχ(G) as an immersion. If true, this would imply that every graph with n vertices and independence number α contains K⌈[Formula ...

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent ...

Computing the size of maximum independent sets is an NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to compute (or approximate) this independence number for random graphs are notoriously ...