Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $d$-stable locally checkable problems on bounded mim-width graphs   In this paper we continue the study of locally checkable problems under the
framework introduced by Bonomo-Braberman and Gonzalez in 2020, by focusing on
graphs of bounded mim-width. We study which restrictions on a locally checkable
problem are necessary in order to be able to solve it efficiently on graphs of
bounded mim-width. To this end, we introduce the concept of $d$-stability of a
check function. The related locally checkable problems contain large classes of
problems, among which we can mention, for example, LCVP problems. We provide an
algorithm which solves all $d$-stable locally checkable problems on graphs of
bounded mim-width in polynomial time and explain how we can include additional
global properties (size of the color classes and connectivity). We explore the
relation between $d$-stable locally checkable problems with the recently
introduced DN-logic (Bergougnoux, Dreier and Jaffke, 2022). We conclude by
listing concrete examples of problems whose complexity on graphs of bounded
mim-width was open so far.

36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org