Block Elimination Distance

We introduce the parameter of block elimination distance as a measure how close graph is to some particular class. Formally, given class $${\mathcal {G}}$$ , {B}}({\mathcal {G}})$$ contains all graphs whose blocks belong and {A}}({\mathcal where removal vertex creates in . Given hereditary we recursively define $${{\mathcal {G}}}^{(k)}$$ so that {G}}^{(0)}={\mathcal and, if $$k\ge 1$$ {G}}^{(k)}={\mathcal {G}}^{(k-1)}))$$ show that, for every non-trivial problem deciding whether $$G\in {\mathcal {G}}^{(k)}$$ NP-complete. focus on case minor-closed study minor obstruction set i.e., minor-minimal not prove size obstructions upper bounded by explicit function k maximum This implies constructively fixed tractable, when parameterized k. Finally, give two operations generate members from {G}}^{(k-1)}$$ this complete {O}}$$ outerplanar graphs.Please check confirm authors Family names have been correctly identified author znur YaŸar Diner.All correctly.Please corresponding identified. Amend necessary.This correct