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Intersection Degree and Bipartite Graphs

Volume 8, Number 2 (2009), 114 - 124

Intersection Degree and Bipartite Graphs

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Abstract

Let S be a homogeneous semigroup and let u1; : : : ;un 2 K[S] be the minimal set of generators of degree 1 of K[S]. We study properties of S when the ideals (ui)\(uj), for all i 6= j, are generated in degree · r, r > 2. As an application, we consider the homogeneous semigroup algebra K[G] associated to a bipartite graph G, we determine a bound for the intersection degree of (ui) \ (uj), i 6= j, related to the length of the cycles of G.