%A Leivaditis, Alexandros
%A Singh, Alexandros
%A Stamoulis, Giannos
%A Thilikos, Dimitrios M.
%A Tsatsanis, Konstantinos
%A Velona, Vasiliki
%D 2019
%T Minor-obstructions for apex sub-unicyclic graphs
%K
%X A graph is {\em sub-unicyclic} if it contains at most one cycle. We also say that a graph $G$ is {\em $k$-apex sub-unicyclic} if it can become sub-unicyclic by removing $k$ of its vertices. We identify 29 graphs that are the minor-obstructions of the class of {$1$-apex} sub-unicyclic graphs, i.e., the set of all minor minimal graphs that do not belong in this class. For bigger values of $k$, we give an exact structural characterization of all the cactus graphs that are minor-obstructions of {$k$-apex} sub-unicyclic graphs and we enumerate them. This implies that, for every $k$, the class of $k$-apex sub-unicyclic graphs has at least $0.34\cdot k^{-2.5}(6.278)^{k}$ minor-obstructions.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1248
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 903-910%V 88
%N 3
%@ 0862-9544
%8 2019-08-01