Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extending Partial Representations of Subclasses of Chordal Graphs   Chordal graphs are intersection graphs of subtrees of a tree T. We
investigate the complexity of the partial representation extension problem for
chordal graphs. A partial representation specifies a tree T' and some pre-drawn
subtrees of T'. It asks whether it is possible to construct a representation
inside a modified tree T which extends the partial representation (i.e, keeps
the pre-drawn subtrees unchanged).
  We consider four modifications of T' and get vastly different problems. In
some cases, it is interesting to consider the complexity even if just T' is
given and no subtree is pre-drawn. Also, we consider three well-known
subclasses of chordal graphs: Proper interval graphs, interval graphs and path
graphs. We give an almost complete complexity characterization.
  We further study the parametrized complexity of the problems when
parametrized by the number of pre-drawn subtrees, the number of components and
the size of the tree T'. We describe an interesting relation with integer
partition problems. The problem Partition is used for all NP-completeness
reductions. The extension of interval graphs when the space in T' is limited is
"equivalent" to the BinPacking problem.

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The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin