Chapter

Integer Programming and Combinatorial Optimization

Volume 3509 of the series Lecture Notes in Computer Science pp 35-50

Approximate Min-max Relations for Odd Cycles in Planar Graphs

  • Samuel FioriniAffiliated withLancaster UniversityGERADUniversité Libre de Bruxelles
  • , Nadia HardyAffiliated withCarnegie Mellon UniversityMcGill University
  • , Bruce ReedAffiliated withCarnegie Mellon UniversityMcGill University
  • , Adrian VettaAffiliated withCarnegie Mellon UniversityMcGill University

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We study the ratio between the minimum size of an odd cycle vertex transversal and the maximum size of a collection of vertex-disjoint odd cycles in a planar graph. We show that this ratio is at most 10. For the corresponding edge version of this problem, Král and Voss [7] recently proved that this ratio is at most 2; we also give a short proof of their result.