Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypohamiltonian planar cubic graphs with girth five   A graph is called hypohamiltonian if it is not hamiltonian but becomes
hamiltonian if any vertex is removed. Many hypohamiltonian planar cubic graphs
have been found, starting with constructions of Thomassen in 1981. However, all
the examples found until now had 4-cycles. In this note we present the first
examples of hypohamiltonian planar cubic graphs with cyclic connectivity five,
and thus girth five. We show by computer search that the smallest members of
this class are three graphs with 76 vertices.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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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: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg