Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: List-Recoloring of Sparse Graphs   Fix a graph $G$, a list-assignment $L$ for $G$, and $L$-colorings $\alpha$
and $\beta$. An $L$-recoloring sequence, starting from $\alpha$, recolors a
single vertex at each step, so that each resulting intermediate coloring is a
proper $L$-coloring. An $L$-recoloring sequence transforms $\alpha$ to $\beta$
if its initial coloring is $\alpha$ and its final coloring is $\beta$. We prove
there exists an $L$-recoloring sequence that transforms $\alpha$ to $\beta$ and
recolors each vertex at most a constant number of times if (i) $G$ is
triangle-free and planar and $L$ is a 7-assignment, or (ii)
$\mathrm{mad}(G)<17/5$ and $L$ is a 6-assignment or (iii)
$\mathrm{mad}(G)<22/9$ and $L$ is a 4-assignment. Parts (i) and (ii) confirm
conjectures of Dvo\v{r}\'{a}k and Feghali.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph