We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterisations of countable graphs and posets with this property; an analogue of Fraı̈ssé’s Theorem; and representations of monoids as endomorphism monoids of such structures. ∗This...

This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called H-homomorphism is given, and transformations from sequential patterns in the H-form and Hform into (H-)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel pro...

This paper computes the Dirac cohomology HD(π) of irreducible unitary Harish-Chandra modules π complex classical groups viewed as real reductive groups. More precisely, representations with nonzero are shown to be unitarily induced from unipotent representations. When nonzero, there is a unique, multiplicity free K-type in contributing HD(π). confirms conjectures formulated by first named autho...

We discuss the construction of a long semi-exact Mayer–Vietoris sequence for homology any finite union open subspaces. This is used to obtain topological conditions representation integral meromorphic n-form on an n-dimensional complex manifold in terms Grothendieck residues. For such exist, it necessary that cycle integration separates set polar hypersurfaces form. The separation condition num...