Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L-factors and adjacent vertex-distinguishing edge-weighting   An edge weighting problem of a graph G is an assignment of an integer weight
to each edge e. Based on edge weighting problem, several types of
vertex-coloring problems are put forward. A simple observation illuminates that
edge weighting problem has a close relationship with special factors of graphs.
In this paper, we obtain several results on the existence of factors with the
pre-specified degrees, which generalizes earlier results in [2, 3]. Using these
results, we investigate edge-weighting problem. In particular, we prove that
every 4-colorable graph admits a vertex-coloring 4-edge-weighting.

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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: econ