TY - JOUR
T1 - Minor-obstructions for apex sub-unicyclic graphs
AU - Leivaditis, Alexandros
AU - Singh, Alexandros
AU - Stamoulis, Giannos
AU - Thilikos, Dimitrios M.
AU - Tsatsanis, Konstantinos
AU - Velona, Vasiliki
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/9/30
Y1 - 2020/9/30
N2 - A graph is sub-unicyclic if it contains at most one cycle. A graph G is 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. 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 k big enough, the class of k-apex sub-unicyclic graphs has at least 0.33⋅k−2.5(6.278)k+1 minor-obstructions.
AB - A graph is sub-unicyclic if it contains at most one cycle. A graph G is 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. 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 k big enough, the class of k-apex sub-unicyclic graphs has at least 0.33⋅k−2.5(6.278)k+1 minor-obstructions.
KW - Graph minors
KW - Obstruction set
KW - Sub-unicyclc graphs
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U2 - 10.1016/j.dam.2020.04.019
DO - 10.1016/j.dam.2020.04.019
M3 - Article
AN - SCOPUS:85084222963
SN - 0166-218X
VL - 284
SP - 538
EP - 555
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -