05064472

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05064472 Rinaldo, Giancarlo Monomial subrings of graphs with loops. Gruber, Peter M. (ed.), Proceedings of the V. international conference of stochastic geometry, convex bodies, empirical measures and applications to engineering, medical and earth sciences, Mondello (Palermo), Italy, September 6--11, 2004. Palermo: Circolo Matem\'atico di Palermo. Supplemento ai Rendiconti del Circolo Matem\'atico di Palermo. Serie II 77, 587-594 (2006). 2006 Palermo: Circolo Matem\'atico di Palermo EN Summary: Let ${\cal G}$ be a graph with loops, we define the monomial subring, $K[{\cal G}]$, associated to ${\cal G}$ and its toric ideal, $P({\cal G})$. We give a complete description of $P(G)$ in terms of the geometric properties of ${\cal G}$. In particular the set of binomials generating $P({\cal G})$ gives information on even cycles, odd cycles passing through a vertex and paths between two vertices.