Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity of colouring problems restricted to unichord-free and
  \{square,unichord\}-free graphs   A \emph{unichord} in a graph is an edge that is the unique chord of a cycle.
A \emph{square} is an induced cycle on four vertices. A graph is
\emph{unichord-free} if none of its edges is a unichord. We give a slight
restatement of a known structure theorem for unichord-free graphs and use it to
show that, with the only exception of the complete graph $K_4$, every
square-free, unichord-free graph of maximum degree~3 can be total-coloured with
four colours. Our proof can be turned into a polynomial time algorithm that
actually outputs the colouring. This settles the class of square-free,
unichord-free graphs as a class for which edge-colouring is NP-complete but
total-colouring is polynomial.

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The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph