Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian cycles in $k$-partite graphs   Chen, Faudree, Gould, Jacobson, and Lesniak determined the minimum degree
threshold for which a balanced $k$-partite graph has a Hamiltonian cycle. We
give an asymptotically tight minimum degree condition for Hamiltonian cycles in
arbitrary $k$-partite graphs in which all parts have at most $n/2$ vertices (a
necessary condition). To do this, we first prove a general result which both
simplifies the process of checking whether a graph $G$ is a robust expander and
gives useful structural information in the case when $G$ is not a robust
expander. Then we use this result to prove that any $k$-partite graph
satisfying the minimum degree condition is either a robust expander or else
contains a Hamiltonian cycle directly.

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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
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: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: stat
1
The categories of this paper are: cs
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The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
29
The categories of this paper are: funct-an