English

Induced subdivisions of $K_{d+1}$ in graphs of high girth

Combinatorics 2026-03-11 v1

Abstract

In this paper, we show that for all k108k\geq 10^8, every graph with minimum degree kk and girth at least 10810^8 contains an induced subdivision of a Kk+1K_{k+1}. This answers a problem asked by K\"uhn and Osthus (originally attributed to Shi).

Keywords

Cite

@article{arxiv.2603.09521,
  title  = {Induced subdivisions of $K_{d+1}$ in graphs of high girth},
  author = {António Girão and Zach Hunter},
  journal= {arXiv preprint arXiv:2603.09521},
  year   = {2026}
}

Comments

11 pages, comments welcome!