Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: List coloring digraphs   The dichromatic number $\vec{\chi}(D)$ 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 Neumann-Lara in 1982, this
digraph invariant shares many properties with the usual chromatic number of
graphs and can be seen as the natural analog of the graph chromatic number. In
this paper, we study the list dichromatic number of digraphs, giving evidence
that this notion generalizes the list chromatic number of graphs. We first
prove that the list dichromatic number and the dichromatic number behave the
same in many contexts, such as in small digraphs (by proving a directed version
of Ohba's Conjecture), tournaments, and random digraphs. We then consider
bipartite digraphs, and show that their list dichromatic number can be as large
as $\Omega(\log_2 n)$. We finally give a Brooks-type upper bound on the list
dichromatic number of digon-free digraphs.

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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph