A representation for the modules of a graph and applications

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A representation for the modules of a graph and applications

Sulamita Klein^I; Jaime L. Szwarcfiter^II

^IInstituto de Matemática and COPPE/Sistemas, UFRJ, CP 68511,21945-970 - Rio de Janeiro, RJ, Brazil, e-mail: [e-mail]

^IIInstituto de Matemática NCE and COPPE/Sistemas, UFRJ, CP 2324,20001-970 - Rio de Janeiro, RJ, Brazil, e-mail: [e-mail]

ABSTRACT

We describe a simple representation for the modules of a graph G. We show that the modules of G are in one-to-one correspondence with the ideals of certain posets. These posets are characterized and shown to be layered posets, that is, transitive closures of bipartite tournaments. Additionaly, we describe applications of the representation. Employing the above correspondence, we present methods for solving the following problems: (i) generate all modules of G, (ii) count the number of modules of G, (iii) find a maximal module satisfying some hereditary property of G and (iv) find a connected non-trivial module of G.

Keywords: graphs, ideals, modules, posets, bipartite tournaments, algorithms

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Publication Dates

• Publication in this collection
  14 Sept 2004
• Date of issue
  Nov 2003