TY - JOUR
T1 - Outerplanar obstructions for a feedback vertex set
AU - Rué, Juanjo
AU - Stavropoulos, Konstantinos S.
AU - Thilikos, Dimitrios M.
PY - 2012/7
Y1 - 2012/7
N2 - For k≥1, let Fk be the class of graphs that contain k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using singularity analysis over the counting series obtained with the Symbolic Method, we prove that |Yk|~C'{dot operator}k-5/2{dot operator}ρ-k where C '{approaches the limit}0.02575057 and ρ -1{approaches the limit}14.49381704 (ρ is the smallest positive root of a quadratic equation).
AB - For k≥1, let Fk be the class of graphs that contain k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using singularity analysis over the counting series obtained with the Symbolic Method, we prove that |Yk|~C'{dot operator}k-5/2{dot operator}ρ-k where C '{approaches the limit}0.02575057 and ρ -1{approaches the limit}14.49381704 (ρ is the smallest positive root of a quadratic equation).
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U2 - 10.1016/j.ejc.2011.09.018
DO - 10.1016/j.ejc.2011.09.018
M3 - Article
AN - SCOPUS:84856950479
SN - 0195-6698
VL - 33
SP - 948
EP - 968
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 5
ER -