English

A Van Kampen type obstruction for string graphs

Combinatorics 2023-08-15 v1

Abstract

In this paper we prove that a graph is a string graph (the intersection graph of curves in the plane) if and only if it admits a drawing in the plane with certain properties. This also allows us to define an algebraic obstruction, similar to the Van Kampen obstruction to embeddability, which must vanish for every string graph. However, unlike in the case of graph planarity this obstruction is incomplete.

Keywords

Cite

@article{arxiv.2308.06833,
  title  = {A Van Kampen type obstruction for string graphs},
  author = {Moshe White},
  journal= {arXiv preprint arXiv:2308.06833},
  year   = {2023}
}

Comments

10 pages, 3 figures

R2 v1 2026-06-28T11:54:41.989Z