Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing list homomorphisms in geometric intersection graphs   A homomorphism from a graph $G$ to a graph $H$ is an edge-preserving mapping
from $V(G)$ to $V(H)$. Let $H$ be a fixed graph with possible loops. In the
list homomorphism problem, denoted by \textsc{LHom}($H$), the instance is a
graph $G$, whose every vertex is equipped with a subset of $V(H)$, called list.
We ask whether there exists a homomorphism from $G$ to $H$, such that every
vertex from $G$ is mapped to a vertex from its list.
  We study the complexity of the \textsc{LHom}($H$) problem in intersection
graphs of various geometric objects. In particular, we are interested in
answering the question for what graphs $H$ and for what types of geometric
objects, the \textsc{LHom}($H$) problem can be solved in time subexponential in
the number of vertices of the instance.
  We fully resolve this question for string graphs, i.e., intersection graphs
of continuous curves in the plane. Quite surprisingly, it turns out that the
dichotomy exactly coincides with the analogous dichotomy for graphs excluding a
fixed path as an induced subgraph [Okrasa, Rz\k{a}\.zewski, STACS 2021].
  Then we turn our attention to subclasses of string graphs, defined as
intersections of fat objects. We observe that the (non)existence of
subexponential-time algorithms in such classes is closely related to the size
$\mathrm{mrc}(H)$ of a maximum reflexive clique in $H$, i.e., maximum number of
pairwise adjacent vertices, each of which has a loop. We study the maximum
value of $\mathrm{mrc}(H)$ that guarantees the existence of a
subexponential-time algorithm for \textsc{LHom}($H$) in intersection graphs of
(i) convex fat objects, (ii) fat similarly-sized objects, and (iii) disks. In
the first two cases we obtain optimal results, by giving matching algorithms
and lower bounds.
  Finally, we discuss possible extensions of our results to weighted
generalizations of \textsc{LHom}($H$).

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th