The dichromatic number of a digraph $ D $ is the minimum number of colors needed to color
its vertices in such a way that each color class induces an acyclic digraph. As it generalizes …

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally
semicomplete if the out-neighbourhood and in-neighbourhood of any vertex induce a …

In the thesis, the coloring of digraphs is studied. The chromatic number of a digraph D is the
smallest integer k so that the vertices of D can be partitioned into at most k sets each of …

Abstract In k-Digraph Coloring we are given a digraph and are asked to partition its vertices
into at most k sets, so that each set induces a DAG. This well-known problem is NP-hard, as …

It seems that combinatorics, and graph theory in particular, reached mathematical maturity
relatively recently. Perhaps as a result of this there are not too many essential stories which …

It has been shown by Bokal et al. that deciding 2-colourability of digraphs is an NP-complete
problem. This result was later on extended by Feder et al. to prove that deciding whether a …

It is well known that for any integers k and g, there is a graph with chromatic number at least
k and girth at least g. In 1960s, Erdos and Hajnal conjectured that for any k and g, there …

We prove that for every oriented graph $ D $ and every choice of positive integers $ k $ and
$\ell $, there exists an oriented graph $ D^* $ along with a surjective homomorphism …

We prove that for every digraph $ D $ and every choice of positive integers $ k $, $\ell $
there exists a digraph $ D^* $ with girth at least $\ell $ together with a surjective acyclic …

Diese Dissertation beschäftigt sich mit Problemstellungen aus der Theorie der endlichen
gerichteten Graphen. Ein (endlicher) gerichteter Graph ist eine binäre Relation, deren …