## Electronic Journal of Probability

### Detecting tampering in a random hypercube

Ross Pinsky

#### Abstract

Consider the random hypercube $H_2^n(p_n)$ obtained from the hypercube $H_2^n$ by deleting any given edge with probabilty $1 -p_n$, independently of all the other edges. A diameter path in $H_2^n$ is a longest geodesic path   in $H_2^n$. Consider the following two ways of tampering with the random graph $H_2^n(p_n)$: (i) choose a diameter path at random and adjoin all of its edges to $H_2^n(p_n)$; (ii)  choose a diameter path at random from among those that start at $0=(0,\cdots, 0)$, and adjoin all of its edges to $H_2^n(p_n)$. We study the question of whether these tamperings are detectable asymptotically as $n\to\infty$.

#### Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 28, 12 pp.

Dates
Accepted: 18 February 2013
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465064253

Digital Object Identifier
doi:10.1214/EJP.v18-2290

Mathematical Reviews number (MathSciNet)
MR3035756

Zentralblatt MATH identifier
1282.05199

Subjects
Secondary: 60C05: Combinatorial probability

Rights

#### Citation

Pinsky, Ross. Detecting tampering in a random hypercube. Electron. J. Probab. 18 (2013), paper no. 28, 12 pp. doi:10.1214/EJP.v18-2290. https://projecteuclid.org/euclid.ejp/1465064253

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