493 research outputs found
Homomorphically Full Oriented Graphs
Homomorphically full graphs are those for which every homomorphic image is
isomorphic to a subgraph. We extend the definition of homomorphically full to
oriented graphs in two different ways. For the first of these, we show that
homomorphically full oriented graphs arise as quasi-transitive orientations of
homomorphically full graphs. This in turn yields an efficient recognition and
construction algorithms for these homomorphically full oriented graphs. For the
second one, we show that the related recognition problem is GI-hard, and that
the problem of deciding if a graph admits a homomorphically full orientation is
NP-complete. In doing so we show the problem of deciding if two given oriented
cliques are isomorphic is GI-complete
A Study of -dipath Colourings of Oriented Graphs
We examine -colourings of oriented graphs in which, for a fixed integer , vertices joined by a directed path of length at most must be
assigned different colours. A homomorphism model that extends the ideas of
Sherk for the case is described. Dichotomy theorems for the complexity of
the problem of deciding, for fixed and , whether there exists such a
-colouring are proved.Comment: 14 page
Alternating Quotients of Fuchsian Groups
It is shown that any finitely generated non-elementary Fuchsian group has
among its homomorphic images all but finitely many of the alternating groups.
This settles in the affirmative a conjecture of Graham Higman.Comment: 20 pages, 7 figure
From self-similar groups to self-similar sets and spectra
The survey presents developments in the theory of self-similar groups leading
to applications to the study of fractal sets and graphs, and their associated
spectra
Multiplicativity of acyclic digraphs
AbstractA homomorphism of a digraph to another digraph is an edge preserving vertex mapping. A digraph W is said to be multiplicative if the set of digraphs which cannot be homomorphically mapped to W is closed under categorical product. We discuss the necessary conditions for a digraph to be multiplicative. Our main result is that almost all acyclic digraphs which have a Hamiltonian path are nonmultiplicative. We conjecture that almost all digraphs are nonmultiplicative
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