text: abstract
  in this paper we present a new width measure for a tree decomposition, minor-matching
  hypertree width, µ-tw, for graphs and hypergraphs, such that bounding the width guarantees
  that set of maximal independent sets has a polynomially-sized restriction to each decomposition bag. the relaxed conditions of the decomposition allow a much wider class of graphs
  and hypergraphs of bounded width compared to other tree decompositions. we show that,
  n
  1
  for fixed k, there are 2(1− k +o(1))( 2 ) n-vertex graphs of minor-matching hypertree width at
  most k. a number of problems including maximum independence set, k-colouring, and
  homomorphism of uniform hypergraphs permit polynomial-time solutions for hypergraphs
  with bounded minor-matching hypertree width and bounded rank. we show that for any
  given k and any graph g, it is possible to construct a decomposition of minor-matching hy3
  pertree width at most o(k 3 ), or to prove that µ-tw(g) > k in time no(k ) . this is done by
  presenting a general algorithm for approximating the hypertree width of well-behaved measures, and reducing µ-tw to such measure. the result relating the restriction of the maximal
  independent sets to a set s with the set of induced matchings intersecting s in graphs, and
  minor matchings intersecting s in hypergraphs, might be of independent interest.