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\iteman{io-port 05064472}
\itemau{Rinaldo, Giancarlo}
\itemti{Monomial subrings of graphs with loops.}
\itemso{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).}
\itemab
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.
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