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                * Princeton Discrete Math Seminar *
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Date: Thursday 2nd November, 3:00 in Fine Hall 224.
 
Speaker: Alex Scott (Oxford)

Title: Packing the discrete torus

Let H be an induced subgraph of the toroidal grid Z_k^m and suppose that 
|V(H)| divides some power of k. We show that if k is even then (for 
large m) the torus has a perfect vertex-packing with induced copies of H.
This extends a result of Gruslys.  On the other hand, when k is odd
and not a prime power, we disprove a conjecture of Gruslys: we show that
there are choices of H such that there is no m for which Z_k^m has a 
perfect vertex-packing with copies of H.

We also discuss edge-packings, and disprove a conjecture of Gruslys,
Leader and Tan by exhibiting a graph H such that H embeds in a
hypercube, but no hypercube has a perfect edge-packing with copies of H.

Joint work with Marthe Bonamy and Natasha Morrison.



Next week: TBA

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