DeepAI AI Chat
Log In Sign Up

Homomorphically Full Oriented Graphs

by   Thomas Bellitto, et al.

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.


page 1

page 2

page 3

page 4


On the dichromatic number of surfaces

In this paper, we give bounds on the dichromatic number χ⃗(Σ) of a surfa...

Orientations without forbidden patterns on three vertices

Given a set of oriented graphs F, a graph G is an F-graph if it admits a...

Chromatic Polynomials of Oriented Graphs

The oriented chromatic polynomial of a oriented graph outputs the number...

On the inversion number of oriented graphs

Let D be an oriented graph. The inversion of a set X of vertices in D co...

On the hull and interval numbers of oriented graphs

In this work, for a given oriented graph D, we study its interval and hu...

Invertibility of digraphs and tournaments

For an oriented graph D and a set X⊆ V(D), the inversion of X in D is th...

Sweeps, polytopes, oriented matroids, and allowable graphs of permutations

A sweep of a point configuration is any ordered partition induced by a l...