All reports by Author Carlos Subi:

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TR08-087
| 31st July 2008
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Tomas Feder, Carlos Subi#### Nearly Tight Bounds on the Number of Hamiltonian Circuits of the Hypercube and Generalizations (revised)

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TR07-063
| 2nd July 2007
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Tomas Feder, Carlos Subi#### Nearly Tight Bounds on the Number of Hamiltonian Circuits of the Hypercube and Generalizations

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TR06-016
| 1st February 2006
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Tomas Feder, Carlos Subi#### Partition into $k$-vertex subgraphs of $k$-partite graphs

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TR06-015
| 1st February 2006
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Tomas Feder, Carlos Subi#### On Barnette's conjecture

Tomas Feder, Carlos Subi

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 ...
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Tomas Feder, Carlos Subi

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 ...
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Tomas Feder, Carlos Subi

The $H$-matching problem asks to partition the vertices of an input graph $G$

into sets of size $k=|V(H)|$, each of which induces a subgraph of $G$

isomorphic to $H$. The $H$-matching problem has been classified as polynomial

or NP-complete depending on whether $k\leq 2$ or not. We consider a variant

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Tomas Feder, Carlos Subi

Barnette's conjecture is the statement that every 3-connected cubic

planar bipartite graph is Hamiltonian. Goodey showed that the conjecture

holds when all faces of the graph have either 4 or 6 sides. We

generalize Goodey's result by showing that when the faces of such a

graph are 3-colored, with adjacent ...
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