# Algorithmic Extensions of Dirac's Theorem

@article{Fomin2022AlgorithmicEO, title={Algorithmic Extensions of Dirac's Theorem}, author={F. Fomin and Petr A. Golovach and Danil Sagunov and Kirill Simonov}, journal={ArXiv}, year={2022}, volume={abs/2011.03619} }

In 1952, Dirac proved the following theorem about long cycles in graphs with large minimum vertex degrees: Every $n$-vertex $2$-connected graph $G$ with minimum vertex degree $\delta\geq 2$ contains a cycle with at least $\min\{2\delta,n\}$ vertices. In particular, if $\delta\geq n/2$, then $G$ is Hamiltonian. The proof of Dirac's theorem is constructive, and it yields an algorithm computing the corresponding cycle in polynomial time. The combinatorial bound of Dirac's theorem is tight in the…

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