Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automated Testing and Interactive Construction of Unavoidable Sets for
  Graph Classes of Small Path-width   We present an interactive framework that, given a membership test for a graph
class $\mathcal{G}$ and a number $k$, finds and tests unavoidable sets for the
class of graphs in $\mathcal{G}$ of path-width at most $k$. We put special
emphasis on the case that $\mathcal{G}$ is the class of cubic graphs and tailor
the algorithm to this case. In particular, we introduce the new concept of
high-degree-first path-decompositions, which yields highly efficient pruning
techniques.
  Using this framework we determine all extremal girth values of cubic graphs
of path-width $k$ for all $k \in \{3,\dots, 10\}$. Moreover, we determine all
smallest graphs which take on these extremal girth values. As a further
application of our framework we characterise the extremal cubic graphs of
path-width 3 and girth 4.

26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga