• Corpus ID: 231786689

A unified half-integral Erd\H{o}s-P\'{o}sa theorem for cycles in graphs labelled by multiple abelian groups

  title={A unified half-integral Erd\H\{o\}s-P\'\{o\}sa theorem for cycles in graphs labelled by multiple abelian groups},
  author={Jochen Pascal Gollin and Kevin Hendrey and Ken-ichi Kawarabayashi and O-joung Kwon and Sang-il Oum},
Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles. However, in 1999, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups, then there is a duality between the maximum… 

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