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DESCRIPTION: A tree with n vertices has at most 95 n/13  minimal dominating
  sets. The growth constant λ= 13 √95≈1.4194908 is best possible. It is obta
 ined in a semi-automatic way as a kind of " dominant eigenvalue " of a bili
 near operation on sextuples that is derived from the dynamic-programming re
 cursion for computing the number of minimal dominating sets of a tree. The 
 core of the method tries to enclose a set of sextuples in a six-dimensional
  geometric body with certain properties\, which depend on some putative val
 ue of λ. This technique is generalizable to other counting problems\, and i
 t raises interesting questions about the "growth" of a general bilinear ope
 ration.   We also derive an output-sensitive algorithm for listing all mini
 mal dominating sets with linear set-up time and linear delay between succes
 sive solutions. 
DTSTAMP:20220119T183600
DTSTART:20220124T141500
CLASS:PUBLIC
LOCATION:Online via Zoom
SEQUENCE:0
SUMMARY:Günter Rote (Freie Universität Berlin): The maximum number of minim
 al dominating sets in a tree
UID:107920019@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220124-L-Rote.html
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