Corpus ID: 195791780

On Hamiltonian cycles in balanced $k$-partite graphs

@article{DeBiasio2019OnHC,
  title={On Hamiltonian cycles in balanced \$k\$-partite graphs},
  author={Louis DeBiasio and Nicholas Spanier},
  journal={arXiv: Combinatorics},
  year={2019}
}
  • Louis DeBiasio, Nicholas Spanier
  • Published 2019
  • Mathematics
  • arXiv: Combinatorics
  • For all integers $k$ with $k\geq 2$, if $G$ is a balanced $k$-partite graph on $n\geq 3$ vertices with minimum degree at least \[ \left\lceil\frac{n}{2}\right\rceil+\left\lfloor\frac{n+2}{2\lceil\frac{k+1}{2}\rceil}\right\rfloor-\frac{n}{k}=\begin{cases} \lceil\frac{n}{2}\rceil+\lfloor\frac{n+2}{k+1}\rfloor-\frac{n}{k} & : k \text{ odd }\\ \frac{n}{2}+\lfloor\frac{n+2}{k+2}\rfloor-\frac{n}{k} & : k \text{ even } \end{cases}, \] then $G$ has a Hamiltonian cycle unless $k=2$ and 4 divides $n$, or… CONTINUE READING

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