Normality of semigroups with some links to graph theory

This is an expository article whose main aim is to introduce nor~nal affine semigroups and its links with other areas such as graph tlleory, linear programming and polyhedral geometry. As an application we derive the classical and generalized ~narriage theorems. 1 Introduction Let A = (a i j) be an integral matrix of order n x q with nonzero distinct columns and let A = {vl,. .. ,v,) be the set of colurnri vectors of A. The integral closure or normalization of the u@ne semigroup associated to A, is defined as: Here & A denotes the rational polyhedral cone in R" given by where & is the set of non negative real numbers, and ZA is the subgroup of Z n generated by A.