Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twin-Width is Linear in the Poset Width   Twin-width is a new parameter informally measuring how diverse are the
neighbourhoods of the graph vertices, and it extends also to other binary
relational structures, e.g. to digraphs and posets. It was introduced just very
recently, in 2020 by Bonnet, Kim, Thomasse and Watrigant. One of the core
results of these authors is that FO model checking on graph classes of bounded
twin-width is in FPT. With that result, they also claimed that posets of
bounded width have bounded twin-width, thus capturing prior result on FO model
checking of posets of bounded width in FPT. However, their translation from
poset width to twin-width was indirect and giving only a very loose
double-exponential bound. We prove that posets of width d have twin-width at
most 9d with a direct and elegant argument, and show that this bound is
asymptotically tight. Specially, for posets of width 2 we prove that in the
worst case their twin-width is also equal 2. These two theoretical results are
complemented with straightforward algorithms to construct the respective
contraction sequence for a given poset.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex