The chromatic number $\overrightarrow {\chi}(D) $ of a digraph $ D $ is the minimum
number of colors needed to color the vertices of $ D $ such that each color class induces an …

It is known (Bollobás (1978)[4]; Kostochka and Mazurova (1977)[12]) that there exist graphs
of maximum degree Δ and of arbitrarily large girth whose chromatic number is at least …

The dichromatic number of a digraph D is the least number k such that the vertex set of D
can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by …

Four proofs of the directed Brooks' Theorem - ScienceDirect Skip to main contentSkip to article
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The dichromatic number χ→(D) χ(D) of a digraph DD is the minimum number of colours
needed to colour the vertices of a digraph such that each colour class induces an acyclic …

The chromatic number of a directed graph D is the minimum number of colors needed to
color the vertices of D such that each color class of D induces an acyclic subdigraph. Thus …

Abstract Let D=(V, A) D=(V,A) be a digraph. We define Δ max (D) Δ_\max(D) as the
maximum of max (d+(v), d−(v))∣ v∈ V {\max(d^+(v),d^-(v))|v∈V\} and Δ min (D) Δ_\min(D) …

Brooks' Theorem states that a connected graph $ G $ of maximum degree $\Delta $ has
chromatic number at most $\Delta $, unless $ G $ is an odd cycle or a complete graph. A …

In this paper, we study colorings of k-partite sparse digraphs. The chromatic number of a
graph G is the smallest integer k such that the vertices of G can be colored with k colors with …

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 …