Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Mohar concerning Kempe equivalence of regular graphs   Let $G$ be a graph with a vertex colouring $\alpha$. Let $a$ and $b$ be two
colours. Then a connected component of the subgraph induced by those vertices
coloured either $a$ or $b$ is known as a Kempe chain. A colouring of $G$
obtained from $\alpha$ by swapping the colours on the vertices of a Kempe chain
is said to have been obtained by a Kempe change. Two colourings of $G$ are
Kempe equivalent if one can be obtained from the other by a sequence of Kempe
changes.
  A conjecture of Mohar (2007) asserts that, for $k \geq 3$, all $k$-colourings
of a $k$-regular graph that is not complete are Kempe equivalent. It was later
shown that all $3$-colourings of a cubic graph that is neither $K_4$ nor the
triangular prism are Kempe equivalent. In this paper, we prove that the
conjecture holds for each $k\geq 4$. We also report the implications of this
result on the validity of the Wang-Swendsen-Koteck\'{y} algorithm for the
antiferromagnetic Potts model at zero-temperature.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph