Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $H$-colouring $P_t$-free graphs in subexponential time   A graph is called $P_t$-free if it does not contain the path on $t$ vertices
as an induced subgraph. Let $H$ be a multigraph with the property that any two
distinct vertices share at most one common neighbour. We show that the
generating function for (list) graph homomorphisms from $G$ to $H$ can be
calculated in subexponential time $2^{O\left(\sqrt{tn\log(n)}\right)}$ for
$n=|V(G)|$ in the class of $P_t$-free graphs $G$. As a corollary, we show that
the number of 3-colourings of a $P_t$-free graph $G$ can be found in
subexponential time. On the other hand, no subexponential time algorithm exists
for 4-colourability of $P_t$-free graphs assuming the Exponential Time
Hypothesis. Along the way, we prove that $P_t$-free graphs have pathwidth that
is linear in their maximum degree.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat