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On the decidability of integer subgraph problems on context-free graph languages

  • Egon Wanke
Commanications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)

Abstract

We show the decidability of integer subgraph problems (ISPs) on context-free sets of graphs L(Γ) defined by hyperedge replacement systems (HRSs) Γ. Additionally, we give a very general characterization of ISPs to be decidable on a set L(Γ). An ISP ∏ consists of a property s and a mapping f . If J is a subgraph of a graph G, then s (G, J) is true or false, and f (G, J) is an integer. We show the decidability of the following problem: Let Π1,...,Π n be n ISPs that fulfill our characterization and let C be a set of conditions (i, o, j) that specify two ISPs Π i and Π j and a compare symbol o ∈ {=, ≠, <, ≤, >, ≥}. Given a context-free set of graphs L defined by a HRS, is there a graph GL that has n subgraphs J1,...,J n such that \(s_{\prod _i }\)(G, J) holds true for i = 1,...,n and \(s_{\prod _i }\)(G, J i ) o \(s_{\prod _j }\)(G, J j ) for each condition (i, o, j)?

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Egon Wanke
    • 1
  1. 1.Mathematik/InformatikUniversität-Gesamthochschule-PaderbornPaderbornFRG

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