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Sparsity pp 227-252 | Cite as

Preservation Theorems

  • Jaroslav Nešetřil
  • Patrice Ossona de Mendez
Chapter
Part of the Algorithms and Combinatorics book series (AC, volume 28)

Abstract

We start with the following observation: If a formula \( \Theta \)expresses a H-coloring problem (i.e.\( \textbf{G}\models \Theta\)if and only if\( G \rightarrow H\)the negated formula \( \rightharpoondown \Theta \)is preserved by homomorphisms:
$$ \textbf{G}\models \rightharpoondown \Phi \;and\; G\rightarrow {G}\prime \quad \Rightarrow \quad {G}\prime \models \rightharpoondown \Phi$$
(1.10)

Keywords

Complete Theory Consistent Theory Elementary Substructure Syntactic Form Order Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Patrice Ossona de Mendez
    • 2
  1. 1.Computer Science Institute of Charles University (IUUK) Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Mathématique Sociales (UMR 8557)CNRS Centre d’Analyse et deParisFrance

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