Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 6-cycle double covers of cubic graphs   A cycle double cover (CDC) of an undirected graph is a collection of the
graph's cycles such that every edge of the graph belongs to exactly two cycles.
We describe a constructive method for generating all the cubic graphs that have
a 6-CDC (a CDC in which every cycle has length 6). As an application of the
method, we prove that all such graphs have a Hamiltonian cycle. A sense of
direction is an edge labeling on graphs that follows a globally consistent
scheme and is known to considerably reduce the complexity of several
distributed problems. In [9], a particular instance of sense of direction,
called a chordal sense of direction (CSD), is studied and the class of
k-regular graphs that admit a CSD with exactly k labels (a minimal CSD) is
analyzed. We now show that nearly all the cubic graphs in this class have a
6-CDC, the only exception being K4.

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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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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: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc