Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multigraphs with $\Delta \ge 3$ are Totally-$(2\Delta-1)$-choosable   The \emph{total graph} $T(G)$ of a multigraph $G$ has as its vertices the set
of edges and vertices of $G$ and has an edge between two vertices if their
corresponding elements are either adjacent or incident in $G$. We show that if
$G$ has maximum degree $\Delta(G)$, then $T(G)$ is $(2\Delta(G)-1)$-choosable.
We give a linear-time algorithm that produces such a coloring. The best
previous general upper bound for $\Delta(G) > 3$ was
$\floor{\frac32\Delta(G)+2}$, by Borodin et al. When $\Delta(G)=4$, our
algorithm gives a better upper bound. When $\Delta(G)\in\{3,5,6\}$, our
algorithm matches the best known bound. However, because our algorithm is
significantly simpler, it runs in linear time (unlike the algorithm of Borodin
et al.).

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat