2 research outputs found
Adjoint functors and tree duality
Get PDFA family T of digraphs is a complete set of obstructions for a digraph H if
for an arbitrary digraph G the existence of a homomorphism from G to H is
equivalent to the non-existence of a homomorphism from any member of T to G. A
digraph H is said to have tree duality if there exists a complete set of
obstructions T consisting of orientations of trees. We show that if H has tree
duality, then its arc graph delta H also has tree duality, and we derive a
family of tree obstructions for delta H from the obstructions for H.
Furthermore we generalise our result to right adjoint functors on categories
of relational structures. We show that these functors always preserve tree
duality, as well as polynomial CSPs and the existence of near-unanimity
functions.Comment: 14 pages, 2 figures; v2: minor revision
