Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Graph Invariant and 2-factorizations of a graph   A spanning subgraph of a graph G is called a [0,2]-factor of G, if for . is a
union of some disjoint cycles, paths and isolate vertices, that span the graph
G. It is easy to get a [0,2]-factor of G and there would be many of
[0,2]-factors for a G.A characteristic number for a [0,2]-factor, which reflect
the number of the paths and isolate vertices in it,is defineted. The
[0,2]-factor of G is called maximum if its characteristic number is minimum,
and is called characteristic number of G.It to be proved that characteristic
number of graph is a graph invariant and a polynomial time algorithm for
computing a maximum [0,2]-factor of a graph G has been given in this paper.
  A [0,2]-factor is Called a 2-factor, if its characteristic number is zero.
That is, a 2-factor is a set of some disjoint cycles, that span G.We propose a
A polynomial time algorism for computing 2-factor from a [0,2]-factor,which can
be got easily.
  A HAMILTON Cycle is a 2-factor, therefore a necessary condition of a HAMILTON
Graph is that, the graph have a 2-factor or the characteristic number of the
graph is zero. The algorism, given in this paper, make it possible to examine
the condition in polynomial time.

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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg