Caracteritzacions de successions gràfiques

Abstract

[en] We say that a sequence is graphical if it defines the sequence of degrees of a simple graph. There are a bunch of different criteria to check whether a sequence is graphical or not. In this project, seven of these criteria are discussed and the equivalence between them is proved. By using this criteria, the relation between the size and the probability of a sequence being graphical is derived, and a function approximating this relation is stated. In order to do so, a software is created which, from a size parameter introduced by the user, finds the percentage of sequences of that size, randomly created, which are graphical.