arXiv 1709.032182017-09-11math.CO

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

Evgeniy Krasko, Igor Labutin, Alexander Omelchenko

英文摘要：

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, Turán 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 $d$

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