We consider non-trivial homomorphisms to reflexive oriented graphs in which some pair of adjacent vertices have the same image. Using a notion convexity for graphs, we study those that do not admit such homomorphisms. fully classify with tree-width $2$ and show it is NP-complete decide if graph admits an orientation does prove analogous results $2$-edge-coloured graphs. apply our on provide new...

It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CYd (d ≥ 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with the changing of some restrictions on the...

We study the list homomorphism and retraction problems for the class of reflexive digraphs (digraphs in which each vertex has a loop). These problems have been intensively studied in the case of undirected graphs, but the situation seems more complex for digraphs. We also focus on an intermediate ‘subretraction’ problem. It turns out that the complexity of the subretraction problem can be class...

Interval graphs admit linear time recognition algorithms and have several elegant forbidden structure characterizations. Interval digraphs can also be recognized in polynomial time and admit a characterization in terms of incidence matrices. Nevertheless, they do not have a known forbidden structure characterization or low-degree polynomial time recognition algorithm. We introduce a new class o...

Within the class of reflexive Banach spaces, we prove a metric characterization asymptotic-c0 spaces in terms bi-Lipschitz invariant which involves metrics that generalize Hamming on k-subsets ℕ. We apply this to show separable, reflexive, and is non-Borel co-analytic. Finally, introduce relaxation property, called asymptotic-subsequential-c0 partial obstruction equi-coarse embeddability sequen...