Outerplanar obstructions for a feedback vertex set

Juanjo Rué, Konstantinos S. Stavropoulos, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Pages (from-to)948-968
Number of pages21
JournalEuropean Journal of Combinatorics
Issue number5
StatePublished - Jul 2012

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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