Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Efficient Domination for $S_{1,1,5}$-Free Bipartite Graphs in
  Polynomial Time   A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient
dominating set} (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 \NP-complete for various
$H$-free bipartite graphs, e.g., Lu and Tang showed that ED is \NP-complete for
chordal bipartite graphs and for planar bipartite graphs; actually, ED is
\NP-complete even for planar bipartite graphs with vertex degree at most 3 and
girth at least $g$ for every fixed $g$. Thus, ED is \NP-complete for
$K_{1,4}$-free bipartite graphs and for $C_4$-free bipartite graphs.
  In this paper, we show that ED can be solved in polynomial time for
$S_{1,1,5}$-free bipartite graphs.

33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: econ