Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When will the crossing number of an alternating link decrease by two via
  a crossing change?   Let $D$ be a reduced alternating diagram of a non-split link $L$ and
$\tilde{L}$ be the link whose diagram is obtained from $D$ by a crossing
change. If $\tilde{L}$ is alternating, then $c(\tilde{L})\leq c(L)-2$. In this
paper we explore when $c(\tilde{L})=c(L)-2$ holds and obtain a simple
sufficient and necessary condition in terms of plane graphs corresponding to
$L$. This result is obtained via analyzing the behavior of the Tutte polynomial
of the signed plane graph corresponding to $\tilde{L}$.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat