Graph theory
standard compliant
MSC

Graph Theory 
Romeo Rizzi

Graphs are a flexible model for core combinatorial problems as arising in various applications. In particular, graphs are encountered in various fields of mathematics, computer science, science in general, and technology.
With this, graph theory is not only fun, but it is also a well established and central area of discrete mathematics of topmost interdisciplinarity.
Some topics we are interested in: matching, factoring, edgecoloring, flows, cycle basis, packing, covering and partitioning, graph classes, algorithmic graph theory.

Computer science
standard compliant
MSC

Combinatorial Algorithms and algorithmic graph theory 
Romeo Rizzi

When we say that our approach to graph theory and combinatorics is algorithmic we not only want to underline the fact that we are most often interested in the obtaining effective algorithms for the problems investigated but also that we indulge unraveling the mathematical problems down till the bottom most level to achieve a most elementary comprehension. Also, we rest on computational complexity as the methodological lighthouse of our research approaches and investigations. This depth and awareness characterizes the strength of the research by our department in Verona. 
Discrete mathematics in relation to computer science 
Romeo Rizzi

Discrete mathematics has a privileged link to computer science, and the converse is also true. As algorithmists, we tangle discrete mathematics in order to give our contribution to computer science. Discrete mathematics in relation to computer science is a huge factory all over the world, and our computer science department here in Verona is well present in all this. 
Theory of computing 
Romeo Rizzi

The theory of computation is the branch of mathematics and computer science that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. In more than one way, this fascinating field has affected our perception of the world and of mathematics itself. In mathematics, it is an eye opener and a source of methodology and philosophical inspiration. This is particularly true for its two main branches of computability theory and computational complexity. 
Polytopes and polyhedra
standard compliant
MSC

Polytopes and Polihedra 
Romeo Rizzi

Polytopes and polyhedra are objects of study in topology, computational geometry, mathematical programming, and combinatorial optimization. The last two perspectives offer tools of operations research which find employment in some of the applied mathematics research lines in Verona. 
Operations research, mathematical programming
standard compliant
MSC

Operations research and management science 
Romeo Rizzi

Operations research is a discipline that deals with the application of advanced analytical methods to help make better decisions.
The terms management science and decision science are sometimes used as more modernsounding synonyms. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or nearoptimal solutions to complex decisionmaking problems. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some realworld objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.
Besides its applications in industry and in management, Operations Research is at the very junction of mathematics and economics. Operations research embodies lots of deep results and theory but, at the same time, it is the archetype of applied mathematics.

Mathematical programming 
Romeo Rizzi

In mathematics, statistics, empirical sciences, computer science, or management science, mathematical optimization (alternatively, mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives. Here, optimization includes finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. Optimization theory, techniques, and algorithms, comprises a large area of applied mathematics. Among the many sectors of mathematical programming, some of those represented in Verona are the following: linear programming, integer linear programming, combinatorial optimization, multiobjective optimization. 