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Article Dans Une Revue Discrete Applied Mathematics Année : 2020

Minor-obstructions for apex sub-unicyclic graphs

Résumé

A graph is {\em sub-unicyclic} if it contains at most one cycle. 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. 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 $0.33\cdot k^{-2.5}(6.278)^{k+1}$ minor-obstructions.
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Dates et versions

hal-03002632 , version 1 (20-11-2020)

Identifiants

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Alexandros Leivaditis, Alexandros Singh, Giannos Stamoulis, Dimitrios M. Thilikos, Konstantinos Tsatsanis, et al.. Minor-obstructions for apex sub-unicyclic graphs. Discrete Applied Mathematics, 2020, 284, pp.538-555. ⟨10.1016/j.dam.2020.04.019⟩. ⟨hal-03002632⟩
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