Outerplanar obstructions for a feedback vertex set

Authors:
Juanjo Rué;Konstantinos S. Stavropoulos;Dimitrios M. Thilikos
Affiliations:
Laboratorie d'Informatique, ícole Polytechnique, 91128 Palaiseau-Cedex, France;Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece;Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece
Venue:
European Journal of Combinatorics
Year:
2012

Citing 6
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Abstract

For k=1, let F"k be the class of graphs that contain k vertices meeting all its cycles. The minor-obstruction set for F"k is the set obs(F"k) containing all minor-minimal graphs that do not belong to F"k. We denote by Y"k the set of all outerplanar graphs in obs(F"k). In this paper, we provide a precise characterization of the class Y"k. Then, using singularity analysis over the counting series obtained with the Symbolic Method, we prove that |Y"k|~C^'@?k^-^5^/^2@?@r^-^k where C^'@?0.02575057 and @r^-^1@?14.49381704 (@r is the smallest positive root of a quadratic equation).