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Corpus ID: 226281837

Algorithmic Extensions of Dirac's Theorem

@article{Fomin2020AlgorithmicEO,
title={Algorithmic Extensions of Dirac's Theorem},
author={F. Fomin and P. Golovach and Danil Sagunov and K. Simonov},
journal={ArXiv},
year={2020},
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… CONTINUE READING