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REPORTS > KEYWORD > HYPERCUBE:
Reports tagged with hypercube:
TR07-063 | 2nd July 2007
Tomas Feder, Carlos Subi

#### Nearly Tight Bounds on the Number of Hamiltonian Circuits of the Hypercube and Generalizations

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 >>>

TR08-087 | 31st July 2008
Tomas Feder, Carlos Subi

#### Nearly Tight Bounds on the Number of Hamiltonian Circuits of the Hypercube and Generalizations (revised)

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 >>>

TR09-046 | 9th May 2009
Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David P. Woodruff

#### Transitive-Closure Spanners of the Hypercube and the Hypergrid

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 >>>

TR10-048 | 24th March 2010
David García Soriano, Arie Matsliah, Sourav Chakraborty, Jop Briet

#### Monotonicity Testing and Shortest-Path Routing on the Cube

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 >>>

TR13-191 | 26th December 2013
Petr Savicky

#### Boolean functions with a vertex-transitive group of automorphisms

A Boolean function is called vertex-transitive, if the partition of the Boolean cube into the preimage of 0 and the preimage of 1 is invariant under a vertex-transitive group of isometric transformations of the Boolean cube. Several constructions of vertex-transitive functions and some of their properties are presented.

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