Geodesic
Minor-obstructions for apex sub-unicyclic graphs
Alexandros Leivaditis1 ; Alexandros Singh2 ; Giannos Stamoulis3 ; Dimitrios M. Thilikos4 ; Konstantinos Tsatsanis2 ; Vasiliki Velona5 ; Alexandros Leivaditis ; Alexandros Singh ; Giannos Stamoulis ; Dimitrios M. Thilikos ; Konstantinos Tsatsanis ; Vasiliki Velona
1Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece
2Inter-university Postgraduate Programme ``Algorithms, Logic, and Discrete Mathematics'' (ALMA), Athens, Greece
3Department of Mathematics, National and Kapodistrian University of Athens and Inter-university Postgraduate Programme ``Algorithms, Logic, and Discrete Mathematics'' (ALMA), Athens, Greece
4AlGCo project-team, LIRMM, Université de Montpellier, CNRS, Montpellier, France
5Politècnica de Catalunya, and Barcelona Graduate School of Mathematics, Barcelona, Spain
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 903-910 
Alexandros Leivaditis; Alexandros Singh; Giannos Stamoulis; Dimitrios M. Thilikos; Konstantinos Tsatsanis; Vasiliki Velona; Alexandros Leivaditis; Alexandros Singh; Giannos Stamoulis; Dimitrios M. Thilikos; Konstantinos Tsatsanis; Vasiliki Velona. Minor-obstructions for apex sub-unicyclic graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 903-910. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a84/
@article{AMUC_2019_88_3_a84,
     author = {Alexandros Leivaditis and Alexandros Singh and Giannos Stamoulis and Dimitrios M. Thilikos and Konstantinos Tsatsanis and Vasiliki Velona and Alexandros Leivaditis and Alexandros Singh and Giannos Stamoulis and Dimitrios M. Thilikos and Konstantinos Tsatsanis and Vasiliki Velona},
     title = { Minor-obstructions for apex sub-unicyclic graphs},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {903--910},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a84/}
}
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AU  - Alexandros Singh
AU  - Giannos Stamoulis
AU  - Dimitrios M. Thilikos
AU  - Konstantinos Tsatsanis
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AU  - Alexandros Leivaditis
AU  - Alexandros Singh
AU  - Giannos Stamoulis
AU  - Dimitrios M. Thilikos
AU  - Konstantinos Tsatsanis
AU  - Vasiliki Velona
TI  - Minor-obstructions for apex sub-unicyclic graphs
JO  - Acta mathematica Universitatis Comenianae
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%A Alexandros Leivaditis
%A Alexandros Singh
%A Giannos Stamoulis
%A Dimitrios M. Thilikos
%A Konstantinos Tsatsanis
%A Vasiliki Velona
%A Alexandros Leivaditis
%A Alexandros Singh
%A Giannos Stamoulis
%A Dimitrios M. Thilikos
%A Konstantinos Tsatsanis
%A Vasiliki Velona
%T Minor-obstructions for apex sub-unicyclic graphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 903-910
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a84/
%F AMUC_2019_88_3_a84

Voir la notice de l'article provenant de la source Comenius University

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.