Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On graphs whose flow polynomials have real roots only   Let $G$ be a bridgeless graph. In 2011 Kung and Royle showed that all roots
of the flow polynomial $F(G,\lambda)$ of $G$ are integers if and only if $G$ is
the dual of a chordal and plane graph. In this article, we study whether a
bridgeless graph $G$ for which $F(G,\lambda)$ has real roots only must be the
dual of some chordal and plane graph. We conclude that the answer of this
problem for $G$ is positive if and only if $F(G,\lambda)$ does not have any
real root in the interval $(1,2)$. We also prove that for any non-separable and
$3$-edge connected $G$, if $G-e$ is also non-separable for each edge $e$ in $G$
and every $3$-edge-cut of $G$ consists of edges incident with some vertex of
$G$, then all roots of $P(G,\lambda)$ are real if and only if either $G\in
\{L,Z_3,K_4\}$ or $F(G,\lambda)$ contains at least $9$ real roots in the
interval $(1,2)$, where $L$ is the graph with one vertex and one loop and $Z_3$
is the graph with two vertices and three parallel edges joining these two
vertices.

36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph