Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameterized Complexity Results for General Factors in Bipartite Graphs
  with an Application to Constraint Programming   The NP-hard general factor problem asks, given a graph and for each vertex a
list of integers, whether the graph has a spanning subgraph where each vertex
has a degree that belongs to its assigned list. The problem remains NP-hard
even if the given graph is bipartite with partition U+V, and each vertex in U
is assigned the list {1}; this subproblem appears in the context of constraint
programming as the consistency problem for the extended global cardinality
constraint. We show that this subproblem is fixed-parameter tractable when
parameterized by the size of the second partite set V. More generally, we show
that the general factor problem for bipartite graphs, parameterized by |V|, is
fixed-parameter tractable as long as all vertices in U are assigned lists of
length 1, but becomes W[1]-hard if vertices in U are assigned lists of length
at most 2. We establish fixed-parameter tractability by reducing the problem
instance to a bounded number of acyclic instances, each of which can be solved
in polynomial time by dynamic programming.

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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th