Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the Grinberg condition in the cycle spaces   Finding a Hamilton graph from simple connected graphs is an important problem
in discrete mathematics and computer science. Grinberg Theorem is a well-known
necessary condition for planar Hamilton graphs. It divides a plane into two
parts: inside and outside faces. The sum of inside faces in a Hamilton graph is
a Hamilton cycle. In this paper, using a basis of the cycle space to represent
a graph and by the Inclusion-Exclusion Principle, we derive the equality with
respect to the inside faces that can be also obtained from Grinberg Theorem. By
further investigating the cycle structure of inside faces, we give a new
combinatorial interpretation to Grinberg's condition, which explains why
Grinberg Theorem is not sufficient for Hamilton graphs. Our results will
improve deriving an efficient condition for Hamilton graphs.

30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess