The elimination distance to some target graph property P is a general graphmodification parameter introduced by Bulian and Dawar . We initiate the study ofelimination distances to graph properties expressible in first-order logic . Wedelimit the problem’s fixed-parameter tractability by identifying sufficientand necessary conditions on the structure of prefixes of first order logicformulas . We complement this statement by showing that such a general statement does not hold for formulas with even slightly moreexpressive prefix structure: there are formulas \phi\in \Pi_3, for whichcomputing elimination distance is W[2] hard. We complement that statement by . showing that that statement doesn’t hold for . formulas with . even slightly . more expressive prefix structure . There are formulas with a more . more than slightly more

Author(s) : Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos