On Factorable Extensions and Subgraphs of Prime Graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1989 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 2, pages 197-218 (issn: 0895-4801, eissn: 1095-7146,

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Authors: Joan Feigenbaum; Ramsey W. Haddad;

doi: 10.1137/0402017

On Factorable Extensions and Subgraphs of Prime Graphs

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Abstract

Summary: Cartesian-factorable extensions and subgraphs of prime graphs are investigated. It is shown that minimal factorable extensions and maximal factorable subgraphs are not unique and that finding them is NP-hard even, in the case of minimal factorable extensions, if the prime graph in question is required to be a tree. Tight bounds on the density of a prime graph's minimal factorable extension are derived. A dynamic programming algorithm is given for finding factorable extensions of certain types of trees.

Keywords

product graphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), Graph theory (including graph drawing) in computer science, tight bounds, Complexity classes (hierarchies, relations among complexity classes, etc.), dynamic programming algorithm, NP- completeness

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