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Minor-obstructions for apex sub-unicyclic graphs

Leivaditis, Alexandros ; Singh, Alexandros ; Stamoulis, Giannos ; Thilikos, Dimitrios M. ; Tsatsanis, Konstantinos ; Velona, Vasiliki

Discrete Applied Mathematics, 2020-09, Vol.284, p.538-555 [Periódico revisado por pares]

Amsterdam: Elsevier B.V

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Título:
Minor-obstructions for apex sub-unicyclic graphs
Autor: Leivaditis, Alexandros ; Singh, Alexandros ; Stamoulis, Giannos ; Thilikos, Dimitrios M. ; Tsatsanis, Konstantinos ; Velona, Vasiliki
Assuntos: Apexes ; Combinatorics ; Graph minors ; Graphs ; Mathematics ; Obstruction set ; Obstructions ; Structural analysis ; Sub-unicyclc graphs
É parte de: Discrete Applied Mathematics, 2020-09, Vol.284, p.538-555
Descrição: 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.
Editor: Amsterdam: Elsevier B.V
Idioma: Inglês

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