In this paper, we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method.

Avant de devenir dessin à graver, la matrice du buriniste Albert Flocon est griffée lignes et figures mettant en tension l’espace plaque cuivre comme un champ forces devenir. L’étude graphie des propos d’Albert permet d’établir aujourd’hui liens entre les formes récurrentes relevées dans ses dessins préparatoires perceptions visuelles synesthètes étudiées par le neurologue américain Richard Cyt...

In this paper we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method.

We present a uniied approach to Graver test sets in LP and IP that is inspired by the critical pair/completion procedure arising in computational algebra. Our algorithms for computing test sets entirely work in the kernel of the problem matrix.

We give an exponential lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph of arbitrary size. Our result is a generalization of the result by Berstein and Onn [2] for the complete bipartite graph K3,r, r ≥ 3.

Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Bu...