Bibliographic Details
| Title: |
Dirac's theorem for random regular graphs. |
| Authors: |
Condon, Padraig, Espuny Díaz, Alberto, Girão, António, Kühn, Daniela, Osthus, Deryk |
| Superior Title: |
Combinatorics, Probability & Computing; Jan2021, Vol. 30 Issue 1, p17-36, 20p |
| Subject Terms: |
REGULAR graphs, RANDOM graphs, RANDOM sets, MAXIMA & minima, LOGICAL prediction |
| Abstract: |
We prove a 'resilience' version of Dirac's theorem in the setting of random regular graphs. More precisely, we show that whenever d is sufficiently large compared to $\epsilon > 0$ , a.a.s. the following holds. Let $G'$ be any subgraph of the random n-vertex d-regular graph $G_{n,d}$ with minimum degree at least $$(1/2 + \epsilon)d$$. Then $G'$ is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. Our result is best possible: firstly the condition that d is large cannot be omitted, and secondly the minimum degree bound cannot be improved. [ABSTRACT FROM AUTHOR] |
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| Database: |
Complementary Index |
