Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On directed local chromatic number, shift graphs, and Borsuk-like graphs   We investigate the local chromatic number of shift graphs and prove that it
is close to their chromatic number. This implies that the gap between the
directed local chromatic number of an oriented graph and the local chromatic
number of the underlying undirected graph can be arbitrarily large. We also
investigate the minimum possible directed local chromatic number of oriented
versions of ``topologically t-chromatic'' graphs. We show that this minimum for
large enough t-chromatic Schrijver graphs and t-chromatic generalized Mycielski
graphs of appropriate parameters is the upper integer part of t/4+1.

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The categories of this paper are: eess
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: stat