title: Décompositions acircuitiques de grands graphes : des aspects algorithmiques aux aspects combinatoires
text: ! CD8 = && EF = =! Æ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
  
  " G!C F N!C F N (!C F N (!C F N! " " = (2 = 1 %! G #=! G'''' N N( N ( (!C F N!C F N ( #! G 9 ( / ( *!C F N ( = ( @!C F N = ( = ( = '. %* 4 " % ) = Æ " # ) 0= % -= # 1H " # 3 = = = % = #
  
  % %
  
  "
  
  %
  
  #.!
  
  " 4
  
  = ='
  
  %
  
  (
  
  #1 " = %
  
  '
  
  % 3
  
  
  
  = " %!
  
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⁄2 & $ + S ) % " = = %' % % " " " = %! 4 " # & & / 0 ) * ) /( C F % CC F C FF N % CC F C FF N 0(. ( $ $ % 3 G *! % "! % C F C F C F C F. =!! 1! " "! C F. = % CF N % C F CF % CF N'% ", % = C F! CF N! CF # $ & ( & 3 G * % 1! = = T CF N T C F. = 0 = 4 3 N % "!!'%
  
  "'# -( * > (') (,( ) #') * > ( ( ) ( # ) ( ) @( * * ( # C F C F ( 3 G * C F. N = T CF N T C F. = 4 # * % " # *% " = = C F * =! C F C F &. = T C F N T CF = T C F N T CF
  
  ! = % " = % #. = % " *" "! % " * % " * " 1! = = " 3 1= " 1! 4. % @ % " 4 0 " % " S 9 " % 4 % % " %. S 9. % % " % 0 * 0 C F 0( 0? % = %.. / % @ @ @. " N. @ @ @. N. @ @ @. * " % " = 1H Æ!'% %' = = 0 - % % " = % = = % CD % / =
  
  &(EF
  
  - $. ) ) C F) ( %.. $ + ".
  
  
  
  = % % %
  
  "
  
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