Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short fans and the 5/6 bound for line graphs   In 2011, the second author conjectured that every line graph $G$ satisfies
$\chi(G)\le \max\{\omega(G),\frac{5\Delta(G)+8}{6}\}$. This conjecture is best
possible, as shown by replacing each edge in a 5-cycle by $k$ parallel edges,
and taking the line graph. In this paper we prove the conjecture. We also
develop more general techniques and results that will likely be of independent
interest, due to their use in attacking the Goldberg--Seymour conjecture.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat