Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clique Separator Decomposition of Hole- and Diamond-Free Graphs and
  Algorithmic Consequences   Clique separator decomposition introduced by Tarjan and Whitesides is one of
the most important graph decompositions. A graph is an {\em atom} if it has no
clique separator. A {\em hole} is a chordless cycle with at least five
vertices, and an {\em antihole} is the complement graph of a hole. A graph is
{\em weakly chordal} if it is hole- and antihole-free. $K_4-e$ is also called
{\em diamond}. {\em Paraglider} has five vertices four of which induce a
diamond, and the fifth vertex sees exactly the two vertices of degree two in
the diamond. In this paper we show that atoms of hole- and diamond-free graphs
(of hole- and paraglider-free graphs, respectively) are either weakly chordal
or of a very specific structure. Hole- and paraglider-free graphs are perfect
graphs. The structure of their atoms leads to efficient algorithms for various
problems.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con