Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Efficient Domination for Some Classes of $H$-Free Bipartite Graphs   A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient
dominating set} (\emph{e.d.s.}\ for short) of $G$ if every vertex of $G$ is
dominated by exactly one vertex of $D$. The \emph{Efficient Domination} (ED)
problem, which asks for the existence of an e.d.s.\ in $G$, is known to be
\NP-complete even for very restricted $H$-free graph classes such as for
$2P_3$-free chordal graphs while it is solvable in polynomial time for
$P_6$-free graphs. Here we focus on $H$-free bipartite graphs: We show that
(weighted) ED can be solved in polynomial time for $H$-free bipartite graphs
when $H$ is $P_7$ or $\ell P_4$ for fixed $\ell$, and similarly for $P_9$-free
bipartite graphs with vertex degree at most 3, and when $H$ is $S_{2,2,4}$.
Moreover, we show that ED is \NP-complete for bipartite graphs with diameter at
most 6.

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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th