Kurosh rank of intersections of subgroups of free products of orderable groups

@article{Antoln2011KuroshRO,
  title={Kurosh rank of intersections of subgroups of free products of orderable groups},
  author={Yago Antol{\'i}n and Armando Martino and Inga Schwabrow},
  journal={arXiv: Group Theory},
  year={2011}
}
We prove that the reduced Kurosh rank of the intersection of two subgroups $H$ and $K$ of a free product of right-orderable groups is bounded above by the product of the reduced Kurosh ranks of $H$ and $K$. In particular, taking the fundamental group of a graph of groups with trivial vertex and edge groups, and its Bass-Serre tree, our Theorem becomes the desired inequality of the usual Strengthened Hanna Neumann conjecture for free groups. 
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