Abstract
A graph-theoretic property is compatible with the rewriting process of hyperedge-replacement graph grammars if for each graph and each derivation of it the property holds just in case the property (or a related property) holds for some specific subgraphs determined by the fibres of the derivation. On the one hand, this leads to proper tests of compatible properties. On the other hand, compatible properties turn out to be decidable for the corresponding graph languages, i.e., the questions
-
(1)
Is there a graph in the generated language having the property?
-
(2)
Do all graphs in the generated language have the property? are decidable for all hyperedge-replacement graph grammars as inputs. In this paper, we introduce the concept of compatible properties, show the compatibility of connectedness, existence of Eulerian paths and cycles, and edge-colorability, and apply the decidability result to these distinguished properties.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
V. Claus, H. Ehrig, G. Rozenberg (eds.): Graph-Grammars and Their Application to Computer Science and Biology, Lect. Not. Comp. Sci. 73, 1979
B.Courcelle: Recognizability and Second Order Definability for Sets of Finite Graphs, Research Report 8634, Bordeaux I University, 1987
H. Ehrig, M. Nagl, A. Rosenfeld, G. Rozenberg (eds.): Graph-Grammars and Their Application to Computer Science, Lect. Not. Comp. Sci. 291, 1987
H. Ehrig, M. Nagl, G. Rozenberg (eds.): Graph-Grammars and Their Application to Computer Science, Lect. Not. Comp. Sci. 153, 1983
A. Habel, H.-J. Kreowski: On Context-Free Graph Languages Generated by Edge Replacement, Lect. Not. Comp. Sci. 153, 143–158, 1983
A. Habel, H.-J. Kreowski: Characteristics of Graph Languages Generated by Edge Replacement, University of Bremen, Comp. Sci. Report No. 3/85, also in: Theor. Comp. Sci. 51, 81–115, 1987
A. Habel, H.-J. Kreowski: May We Introduce to You: Hyperedge Replacement, Lect. Not. Comp. Sci. 291, 15–26, 1987
A. Habel, H.-J. Kreowski: Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement, Proc. STACS'87, Lect. Not. Comp. Sci. 247, 207–219, 1987
A. Habel, H.-J. Kreowski, W. Vogler: Metatheorems for Decision Problems on Hyperedge Replacement Graph Languages, Techn. Report, short version in: Bull. EATCS 33, 55–62, 1987
H.-J. Kreowski: Rule Trees Can Help to Escape Hard Graph Problems, unpublished
C. Lautemann: Decomposition Trees: Structured Graph Representation and Efficient Algorithms, Proc. CAAP'88, Lect. Not. Comp. Sci. 299, 28–39, 1988
T. Lengauer: Efficient Solution of Biconnectivity Problems on Hierarchically Defined Graphs, Proc. WG'85, Trauner Verlag, Linz, 201–215, 1985
T. Lengauer, E. Wanke: Efficient Analysis of Graph Properties on Context-Free Graph Languages, Proc. ICALP'88, Lect. Not. Comp. Sci. 317, 379–393, 1988
G. Rozenberg, E. Welzl: Boundary NLC Graph Grammars — Basic Definitions, Normal Forms, and Complexity, Inf. Contr. 69, 136–167, 1986
G. Rozenberg, E. Welzl: Graph Theoretic Closure Properties of the Family of Boundary NLC Graph Languages, Acta Informatica 23, 289–309, 1986
A.O. Slisenko: Context-Free Graph Grammars as a Tool for Describing Polynomial-time Subclasses of Hard Problems, Inf. Proc. Lett. 14, 52–56, 1982
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Habel, A. (1989). Graph-theoretic properties compatible with graph derivations. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_33
Download citation
DOI: https://doi.org/10.1007/3-540-50728-0_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50728-4
Online ISBN: 978-3-540-46076-3
eBook Packages: Springer Book Archive