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SUMMARY:Independent spanning trees in the hypercube - Benedict Randall Sha
 w (Cambridge)
DTSTART:20250605T133000Z
DTEND:20250605T143000Z
UID:TALK232495@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:We say two spanning trees of a graph are completely independen
 t if their edge sets are disjoint\, and for each pair of vertices\, the pa
 ths between them in each spanning tree do not have any other vertex in com
 mon. Pai and Chang constructed two such spanning trees in the hypercube Q_
 n for sufficiently large n\, while Kandekar and Mane recently showed there
  are 3 pairwise completely independent spanning trees in hypercubes Q_n fo
 r sufficiently large n. We prove that for each k\, there exist k completel
 y independent spanning trees in Q_n for sufficiently large n. In fact\, we
  show that there are (1/12+o(1))n spanning trees in Q_n.
LOCATION:MR12
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