Preservation Theorems

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)

Preserve: to prepare so as to resist to decomposition.