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On Generalized Graph Ideals of Complete Bipartite Graphs
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Let S = K[X1, . . . , Xn; Y1, . . . , Ym] be the polynomial ring in two sets of variables over a field K. Using the notion of linear quotients, we investigate significative classes of graph ideals of S that have a linear resolution, namely the generalized graph ideals, in order to compute standard algebraic invariants of S modulo such ideals. Moreover we are able to determine the structure of the ideals of vertex covers for such generalized graph ideals.
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