Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eulerian graphs and local complementation   We define pure graphs, invertible graphs, and the notion of complementation
of bicoloured graphs. The study of pure graphs is motivated by two conjectures
about the transition systems of eulerian graphs and by the Cycle Double Cover
Conjecture. We show how substitution rules can be used to determine when two
complementation words produce the same graph. For bicoloured graphs,
complementation words give way to complementation sets. The invertible graphs
(bicoloured graphs whose vertex set is a complementation set) are shown to have
the property that their inverse has the same automorphisms. The property of
being invertible can also be defined for non-coloured graphs by endowing them
with their natural colouring. It is proposed that a characterization of pure
graphs would contribute to establish the truth of the Cycle Double Cover
Conjecture. We show how pure graphs have essential factorizations into
primitive pure graphs. The four primitive pure parity classes are presented.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: alg-geom