We consider the asymptotic behavior of the second and higher gonalities of an Erdős-Rényi random graph and provide upper bounds for both via the probabilistic method. Our results suggest that for sufficiently large n, the second gonality of an Erdős-Rényi random Graph G(n, p) is strictly less than and asymptotically equal to the number of vertices under a suitable restriction of the probability...

Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor (EG) under the assumption of full visibility. For this class of random graphs we establish a zero-one law for the existence of triangles, and identify the corresponding critical scaling. This zero-one law exhibits significant differences with the corresponding result in Erdős-Rényi grap...

Estimation of Shannon and Rényi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on the number of samples to estimate these entropies have been established in the classical setting, while little is known about their quantum counterparts. In t...