Sparsity pp 227-252 | Cite as

Preservation Theorems

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


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:
$$ \textbf{G}\models \rightharpoondown \Phi \;and\; G\rightarrow {G}\prime \quad \Rightarrow \quad {G}\prime \models \rightharpoondown \Phi$$


Complete Theory Consistent Theory Elementary Substructure Syntactic Form Order Formula 
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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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