View in EDS

The recognizability of sets of graphs is a robust property

Saved in:
Bibliographic Details
Title: The recognizability of sets of graphs is a robust property
Authors: Courcelle, Bruno1 bruno.courcelle@labri.fr, Weil, Pascal2 pascal.weil@labri.fr
Source: Theoretical Computer Science. Sep2005, Vol. 342 Issue 2/3, p173-228. 56p.
Subjects: Algebra, Mathematical analysis, Mathematics, Graphic methods
Abstract: Abstract: Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of context-free sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) context-free graph grammars, to Vertex Replacement (VR) context-free graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifier-free formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HR-recognizability and VR-recognizability coincide. The same combinatorial condition equates HR-context-free and VR-context-free sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures. [Copyright &y& Elsevier]
Copyright of Theoretical Computer Science is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:Abstract: Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of context-free sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) context-free graph grammars, to Vertex Replacement (VR) context-free graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifier-free formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HR-recognizability and VR-recognizability coincide. The same combinatorial condition equates HR-context-free and VR-context-free sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures. [Copyright &y& Elsevier]
ISSN:03043975
DOI:10.1016/j.tcs.2005.03.018