Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recolouring weakly chordal graphs and the complement of triangle-free
  graphs   For a graph $G$, the $k$-recolouring graph $\mathcal{R}_k(G)$ is the graph
whose vertices are the $k$-colourings of $G$ and two colourings are joined by
an edge if they differ in colour on exactly one vertex. We prove that for all
$n \ge 1$, there exists a $k$-colourable weakly chordal graph $G$ where
$\mathcal{R}_{k+n}(G)$ is disconnected, answering an open question of Feghali
and Fiala. We also show that for every $k$-colourable $3K_1$-free graph $G$,
$\mathcal{R}_{k+1}(G)$ is connected with diameter at most $4|V(G)|$.

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph