Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A zero-free interval for chromatic polynomials of graphs with 3-leaf
  spanning trees   It is proved that if $G$ is a graph containing a spanning tree with at most
three leaves, then the chromatic polynomial of $G$ has no roots in the interval
$(1,t_1]$, where $t_1 \approx 1.2904$ is the smallest real root of the
polynomial $(t-2)^6 +4(t-1)^2(t-2)^3 -(t-1)^4$. We also construct a family of
graphs containing such spanning trees with chromatic roots converging to $t_1$
from above. We employ the Whitney $2$-switch operation to manage the analysis
of an infinite class of chromatic polynomials.

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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio