Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: FPT algorithms to recognize well covered graphs   Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a
maximum minimal vertex covers of $G$, respectively. We say that $G$ is well
covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same
size). Determining if a graph is well covered is a coNP-complete problem. In
this paper, we obtain $O^*(2^{vc})$-time and $O^*(1.4656^{vc^+})$-time
algorithms to decide well coveredness, improving results of Boria et. al.
(2015). Moreover, using crown decomposition, we show that such problems admit
kernels having linear number of vertices. In 2018, Alves et. al. (2018) proved
that recognizing well covered graphs is coW[2]-hard when the independence
number $\alpha(G)=n-vc(G)$ is the parameter. Contrasting with such
coW[2]-hardness, we present an FPT algorithm to decide well coveredness when
$\alpha(G)$ and the degeneracy of the input graph $G$ are aggregate parameters.
Finally, we use the primeval decomposition technique to obtain a linear time
algorithm for extended $P_4$-laden graphs and $(q,q-4)$-graphs, which is FPT
parameterized by $q$, improving results of Klein et al (2013).

2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat