Proof of `Taking minors and preservation under complements` (2nd statement)
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
, (1) ⇒ (2). A minor-closed class is closed under deleting edges and under
contracting edges, and hom(F, Ḡ) is a signed sum of homomorphism counts from the graphs
obtained from by deleting a set of edges and contracting another, all of which are minors
of .