Dirac's theorem for random graphs

@article{Lee2012DiracsTF,
  title={Dirac's theorem for random graphs},
  author={Choongbum Lee and Benny Sudakov},
  journal={Random Struct. Algorithms},
  year={2012},
  volume={41},
  pages={293-305}
}
A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least dn/2e is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if p log n/n, then a.a.s. every subgraph ofG(n, p) with minimum degree at least (1/2+o(1))np is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge… CONTINUE READING
Highly Cited
This paper has 64 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 22 extracted citations

65 Citations

01020'13'15'17'19
Citations per Year
Semantic Scholar estimates that this publication has 65 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 28 references

Local resilience of graphs

Random Struct. Algorithms • 2008
View 4 Excerpts
Highly Influenced

Hamiltonian circuits in random graphs

Discrete Mathematics • 1976
View 4 Excerpts
Highly Influenced

Bandwidth theorem for sparse graphs

T. Łuczak S. Janson, A. Rucinski
J Comb Theory , Ser B • 2012