Bounding the mim‐width of hereditary graph classes

A large number of NP-hard graph problems are solvable in XP time when parameterized by some width parameter. Hence, solving on special classes, it is helpful to know if the class under consideration has bounded width. In this paper we consider maximum-induced matching (mim-width), a particularly general parameter that algorithmic applications whenever decomposition “quickly computable” for consideration. We start extending toolkit proving (un)boundedness mim-width classes. By combining our new techniques with known ones then initiate systematic study into bounding from perspective hereditary and make comparison clique-width, more restrictive been well studied. prove given H, H-free graphs only clique-width. show same not true ( H 1 , 2 ) -free graphs. identify several classes having unbounded but mim-width; moreover, branch constant can be found polynomial these results have implications: input restricted such graphs, many become polynomial-time solvable, including classical problems, as k- Colouring Independent Set, domination-type Locally Checkable Vertex Subset Partitioning (LC-VSVP) distance versions LC-VSVP name just few. also showing that, certain mim-width. Boundedness clique-width implies boundedness cases present summary theorems current state art particular, classify all pairs ∣ V + ≤ 8. When connected except one remaining infinite family few isolated cases.