We conjecture that for every perfect matching $M$ of the $d$-dimensional
$n$-vertex hypercube, $d\geq 2$, there exists a second perfect matching $M'$
such that the union of $M$ and $M'$ forms a Hamiltonian circuit of the
$d$-dimensional hypercube. We prove this conjecture in the case where there are
two dimensions ... more >>>

It has been shown that for every perfect matching $M$ of the $d$-dimensional
$n$-vertex hypercube, $d\geq 2, n=2^d$, there exists a second perfect matching
$M'$ such that the union of $M$ and $M'$ forms a Hamiltonian circuit of the
$d$-dimensional hypercube. We prove a generalization of a special case of ... more >>>

Given a directed graph $G = (V,E)$ and an integer $k \geq 1$, a $k$-transitive-closure-spanner ($k$-TC-spanner) of $G$ is a directed graph $H = (V, E_H)$ that has (1) the same transitive-closure as $G$ and (2) diameter at most $k$. Transitive-closure spanners were introduced in \cite{tc-spanners-soda} as a common abstraction ... more >>>

We study the problem of monotonicity testing over the hypercube. As
previously observed in several works, a positive answer to a natural question about routing
properties of the hypercube network would imply the existence of efficient
monotonicity testers. In particular, if any $\ell$ disjoint source-sink pairs
on the directed hypercube ... more >>>