code: def __insert_branch(u, v, dfs_data):
      
      w = L1(v, dfs_data)
      d_u = D(u, dfs_data)
      d_w = D(w, dfs_data)
  
      # Embed uw
      successful = __embed_frond(u, w, dfs_data)
      if not successful:
          return False
  
      # Embed a branch marker uu on the side opposite to uw, in the same frond block
      #successful = __embed_frond(u, v, dfs_data, as_branch_marker=True)
      successful = __embed_frond(u, u, dfs_data, as_branch_marker=True)
      if not successful:
          return False
  
      return True
docs: Embeds a branch Bu(v) (as described on page 22 of the paper). Returns whether the embedding was successful.