Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Checkerboard embeddings of *-graphs into nonorientable surfaces   This paper considers *-graphs in which all vertices have degree 4 or 6, and
studies the question of calculating the genus of nonorientable surfaces into
which such graphs may be embedded. In a previous paper by the authors, the
problem of calculating whether a given *-graph in which all vertices have
degree 4 or 6 admits a Z2-homologically trivial embedding into a given
orientable surface was shown to be equivalent to a problem on matrices. Here we
extend those results to nonorientable surfaces. The embeddability condition
that we obtain yields quadratic-time algorithms to determine whether a *-graph
with all vertices of degree 4 or 6 admits a Z2-homologically trivial embedding
into the projective plane or into the Klein bottle.

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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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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: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat