Bibliographic Details
| Title: |
Dirac's theorem for random graphs. |
| Authors: |
Lee, Choongbum, Sudakov, Benny |
| Superior Title: |
Random Structures & Algorithms; Oct2012, Vol. 41 Issue 3, p293-305, 13p |
| Abstract: |
A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{align*}\left\lceil n/2 \right\rceil\end{align*} \end{document} 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 of G( n, p) with minimum degree at least (1/2 + o (1)) n p is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge probability p and the value of the constant 1/2 are asymptotically best possible. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 [ABSTRACT FROM AUTHOR] |
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| Database: |
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