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Let G be a connected bipartite graph. We present an approach to the computation of the canonical module of the edge subring associated to G using linear programming.

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge… (More)

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas to the more general space of rooted and labeled trees. We redefine concepts such as tree-line and forward principal… (More)

Given an integer weighted bipartite graph {G = (U ⊔ V, E), w : E → Z} we consider the problems of finding all the edges that occur in some minimum weight matching of maximum cardinality and enumerating all the minimum weight perfect matchings. Moreover, we construct a subgraph Gcs of G which depends on an ǫ-optimal solution of the dual linear program… (More)

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