Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on module-composed graphs   In this paper we consider module-composed graphs, i.e. graphs which can be
defined by a sequence of one-vertex insertions v_1,...,v_n, such that the
neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of
the graph defined by vertices v_1,..., v_{i-1}.
  We show that module-composed graphs are HHDS-free and thus homogeneously
orderable, weakly chordal, and perfect. Every bipartite distance hereditary
graph, every (co-2C_4,P_4)-free graph and thus every trivially perfect graph is
module-composed. We give an O(|V_G|(|V_G|+|E_G|)) time algorithm to decide
whether a given graph G is module-composed and construct a corresponding
module-sequence.
  For the case of bipartite graphs, module-composed graphs are exactly distance
hereditary graphs, which implies simple linear time algorithms for their
recognition and construction of a corresponding module-sequence.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas