177 research outputs found
Homogeneous 2-partite digraphs
We call a 2-partite digraph D homogeneous if every isomorphism between finite
induced subdigraphs that respects the 2-partition of D extends to an
automorphism of D that does the same. In this note, we classify the homogeneous
2-partite digraphs.Comment: 5 page
Countable connected-homogeneous digraphs
A digraph is connected-homogeneous if every isomorphism between two finite
connected induced subdigraphs extends to an automorphism of the whole digraph.
In this paper, we completely classify the countable connected-homogeneous
digraphs.Comment: 49 page
The conjugacy problem for automorphism groups of countable homogeneous structures
We consider the conjugacy problem for the automorphism groups of a number of
countable homogeneous structures. In each case we find the precise complexity
of the conjugacy relation in the sense of Borel reducibility
On Ramsey properties of classes with forbidden trees
Let F be a set of relational trees and let Forbh(F) be the class of all
structures that admit no homomorphism from any tree in F; all this happens over
a fixed finite relational signature . There is a natural way to expand
Forbh(F) by unary relations to an amalgamation class. This expanded class,
enhanced with a linear ordering, has the Ramsey property.Comment: Keywords: forbidden substructure; amalgamation; Ramsey class; partite
method v2: changed definition of expanded class; v3: final versio
Magic graphs and the faces of the Birkhoff polytope
Magic labelings of graphs are studied in great detail by Stanley and Stewart.
In this article, we construct and enumerate magic labelings of graphs using
Hilbert bases of polyhedral cones and Ehrhart quasi-polynomials of polytopes.
We define polytopes of magic labelings of graphs and digraphs. We give a
description of the faces of the Birkhoff polytope as polytopes of magic
labelings of digraphs.Comment: 9 page
- …