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 ...

In this work, we investigate the classification of Morse-Bott functions from S-2 to S-1, up to topological conjugacy. We give a complete topological invariant of simple Morse-Bott functions f : S-2 -> S-1. The invariant ...

We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable ...

We show how to associate with each graph with a certain property (positivity) a family of simply connected solvable Lie groups endowed with left-invariant Riemannian metrics that are Ricci solitons (called solvsolitons). ...