<i>k</i> -apices of Minor-closed Graph Classes. II. Parameterized Algorithms

Let ???? be a minor-closed graph class. We say that G is k -apex of if contains set S at most vertices such G\S belongs to . denote by ???? ( ) the all graphs are -apices In first paper this series, we obtained upper bounds on size in minor-obstruction ), i.e., minor-minimal not belonging ). article, provide an algorithm that, given n vertices, runs time 2 poly (k) ? 3 and either returns certifying ? or reports ? Here polynomial function whose degree depends maximum special case where excludes some apex as minor, give alternative running -time.