Minor-Obstructions for Apex Sub-unicyclic Graphs
Combinatorics
2019-02-07 v1
Abstract
A graph is sub-unicyclic if it contains at most one cycle. We also say that a graph is -apex sub-unicyclic if it can become sub-unicyclic by removing of its vertices. We identify 29 graphs that are the minor-obstructions of the class of -apex sub-unicyclic graphs, i.e., the set of all minor minimal graphs that do not belong in this class. For bigger values of , we give an exact structural characterization of all the cactus graphs that are minor-obstructions of -apex sub-unicyclic graphs and we enumerate them. This implies that, for every , the class of -apex sub-unicyclic graphs has at least minor-obstructions.
Keywords
Cite
@article{arxiv.1902.02231,
title = {Minor-Obstructions for Apex Sub-unicyclic Graphs},
author = {Alexandros Leivaditis and Alexandros Singh and Giannos Stamoulis and Dimitrios Thilikos and Konstantinos Tsatsanis and Vasiliki Velona},
journal= {arXiv preprint arXiv:1902.02231},
year = {2019}
}