# Hamiltonicity in balanced*k*-partite graphs

Original Papers

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## Abstract

One of the earliest results about hamiltonian graphs was given by Dirac. He showed that if a graph then

*G*has order*p*and minimum degree at least\(\frac{p}{2}\) then*G*is hamiltonian. Moon and Moser showed that a balanced bipartite graph (the two partite sets have the same order)*G*has order*p*and minimum degree more than\(\frac{p}{4}\) then*G*is hamiltonian. In this paper, their idea is generalized to*k*-partite graphs and the following result is obtained: Let*G*be a balanced*k*-partite graph with order*p = kn.*If the minimum degree$$\delta (G) > \left\{ {\begin{array}{*{20}c} {\left( {\frac{k}{2} - \frac{1}{{k + 1}}} \right)n if k is odd } \\ {\left( {\frac{k}{2} - \frac{2}{{k + 2}}} \right)n if k is even} \\ \end{array} } \right.$$

*G*is hamiltonian. The result is best possible.## Keywords

Early Result Bipartite Graph Minimum Degree Hamiltonian Graph Balance Bipartite Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.Dirac, G.: Some theorems on abstract graphs. Proc. London Math Soc.
**2**, 69–81 (1952)Google Scholar - 2.Moon, J., Moser L.: On hamiltonian bipartite graphs. Israel J. Math
**1**, 163–165 (1963)Google Scholar - 3.Ore, O.: Note on hamiltonian circuits. Amer. Math Monthly
**67**, 55 (1960)Google Scholar

## Copyright information

© Springer-Verlag 1995