Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete $k$-partite Graphs

Evgeniy Krasko; Igor Labutin; Alexander Omelchenko

Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete $k$-partite Graphs

Combinatorics 2017-09-12 v1

Authors: Evgeniy Krasko , Igor Labutin , Alexander Omelchenko

Abstract

We enumerate labelled and unlabelled Hamiltonian cycles in complete $n$ -partite graphs $K_{d,d,\ldots,d}$ having exactly $d$ vertices in each part (in other words, Tur\'an graphs $T(nd, n))$ . We obtain recurrence relations that allow us to find the exact values $b_{n}^{(d)}$ of such cycles for arbitrary $n$ and $d$

Keywords

Hamiltonian cycles complete multipartite graphs labelled enumeration unlabelled enumeration Turán graphs recurrence relations

Cite

@article{arxiv.1709.03218,
  title  = {Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete $k$-partite Graphs},
  author = {Evgeniy Krasko and Igor Labutin and Alexander Omelchenko},
  journal= {arXiv preprint arXiv:1709.03218},
  year   = {2017}
}

Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete $k$-partite Graphs

Abstract

Keywords

Cite

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