A representation for the modules of a graph and applications

Journal of the Brazilian Computer Society

Univeridade Federal do Rio de Janeiro, Rio de Janeiro, Brazil¹  Klein, Sulamita¹  Szwarcfiter, Jaime L.¹ 

关键词: graphs;    ideals;    modules;    posets;    bipartite tournaments;    algorithms;   

DOI  :  10.1590/S0104-65002003000200002

学科分类：农业科学（综合）

来源: Springer U K

【 摘 要 】

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.

【 授权许可】

Unknown