Grid recognition: Classical and parameterized computational perspectives

Over the past few decades, a large body of works studied (in)tractability various computational problems on grid graphs, which often yield substantially faster algorithms than general graphs. Unfortunately, recognition graph is hard—it was shown to be NP-hard already in 1987. In this paper, we provide several positive results regard framework parameterized complexity. Specifically, our contribution threefold. First, show that problem FPT by k+mcc where mcc maximum size connected component G. Second, present new parameterization, denoted aG, relating distance geometric distance. We para-NP-hard but aG trees, as well k+aG. Third, k×r graphs pathwidth 2 k=3.