Year: 2019
Type: article
Abstract: Chen et al determined the minimum degree threshold for which a balanced ‐partite graph has a Hamiltonian cycle. We give an asymptotically tight minimum degree condition for Hamiltonian cycles in arbitrary ‐partite graphs in that all parts have at most vertices (a necessary condition). To do this, we first prove a general result that both simplifies the process of checking whether a graph is a robust expander and gives useful structural information in the case when is not a robust expander. Then we use this result to prove that any ‐partite graph satisfying the minimum degree condition is either a robust expander or else contains a Hamiltonian cycle directly.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.22508
Institution: Miami University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2942951167